tag:blogger.com,1999:blog-12306752321011808772018-03-06T02:58:48.140-08:00cond-mat.stat-mech - Statistical MechanicsSite for <a href="http://communitypeerreview.blogspot.com/">Community Peer Review</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.comBlogger4902125tag:blogger.com,1999:blog-1230675232101180877.post-53633605647501836402013-08-06T00:01:00.019-07:002013-08-06T00:01:45.141-07:001308.0660 (Hideyuki Suzuki)<h2 class="title"><a href="http://arxiv.org/abs/1308.0660">Monte Carlo simulation of classical spin models with chaotic billiards</a> [<a href="http://arxiv.org/pdf/1308.0660">PDF</a>]</h2>Hideyuki Suzuki<a name='more'></a><blockquote class="abstract">It has recently been shown that the computing abilities of Boltzmann machines, or Ising spin-glass models, can be implemented by chaotic billiard dynamics without any use of random numbers. In this paper, we further numerically investigate the capabilities of the chaotic billiard dynamics as a deterministic alternative to random Monte Carlo methods by applying it to classical spin models in statistical physics. First, we verify that the billiard dynamics can yield samples that converge to the true distribution of the Ising model on a small lattice, and we show that it appears to have the same convergence rate as random Monte Carlo sampling. Second, we apply the billiard dynamics to finite-size scaling analysis of the critical behavior of the Ising model and show that the phase transition point and the critical exponents are correctly obtained. Third, we extend the billiard dynamics to spins that take more than two states and show that it can be applied successfully to the Potts model. We also discuss the possibility of extensions to continuous-valued models such as the XY model.</blockquote>View original: <a href="http://arxiv.org/abs/1308.0660">http://arxiv.org/abs/1308.0660</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-1230675232101180877.post-46209836875558818662013-08-06T00:01:00.017-07:002013-08-06T00:01:43.924-07:001308.0712 (F. Intravaia et al.)<h2 class="title"><a href="http://arxiv.org/abs/1308.0712">Quantum friction and non-equilibrium fluctuation theorems</a> [<a href="http://arxiv.org/pdf/1308.0712">PDF</a>]</h2>F. Intravaia, R. O. Behunin, D. A. R. Dalvit<a name='more'></a><blockquote class="abstract">We use general concepts of non-equilibrium statistical mechanics to compute the quantum frictional force on an atom in steady motion above a surface. We derive the frictional force using a non-equilibrium fluctuation-dissipation relation, and compare with that computed with the quantum regression theorem. We show that beyond the weak coupling limit, quantum regression fails to predict the correct stationary atom-surface interaction as given by fluctuation-dissipation, both in and out of equilibrium, mainly due to the broadband nature of fluctuation-induced interactions.</blockquote>View original: <a href="http://arxiv.org/abs/1308.0712">http://arxiv.org/abs/1308.0712</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-1230675232101180877.post-74582192597018715862013-08-06T00:01:00.015-07:002013-08-06T00:01:41.682-07:001308.0734 (Christophe Chatelain)<h2 class="title"><a href="http://arxiv.org/abs/1308.0734">Griffiths phase and critical behavior of the 2D Potts models with<br /> long-range correlated disorder</a> [<a href="http://arxiv.org/pdf/1308.0734">PDF</a>]</h2>Christophe Chatelain<a name='more'></a><blockquote class="abstract">The $q$-state Potts model with a long-range correlated disorder is studied by means of large-scale Monte Carlo simulations for $q=2,4,8$ and 16. Evidence is given of the existence of a Griffiths phase, where the thermodynamic quantities display an algebraic Finite-Size Scaling, in a finite range of temperatures around the self-dual point. The critical exponents are shown to depend on both the temperature and the exponent of the algebraic decay of disorder correlations, but not on the number of states of the Potts model. The mechanism leading to the violation of hyperscaling relations is observed in the entire Griffiths phase.</blockquote>View original: <a href="http://arxiv.org/abs/1308.0734">http://arxiv.org/abs/1308.0734</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-1230675232101180877.post-68371391587867172342013-08-06T00:01:00.013-07:002013-08-06T00:01:40.661-07:001308.0750 (M. Burrello et al.)<h2 class="title"><a href="http://arxiv.org/abs/1308.0750">Topological phase transitions driven by non-Abelian gauge potentials in<br /> optical square lattices</a> [<a href="http://arxiv.org/pdf/1308.0750">PDF</a>]</h2>M. Burrello, I. C. Fulga, E. Alba, L. Lepori, A. Trombettoni<a name='more'></a><blockquote class="abstract">We analyze a tight-binding model of ultracold fermions loaded in an optical square lattice and subjected to a synthetic non-Abelian gauge potential featuring both a magnetic field and a translational invariant SU(2) term. We consider in particular the effect of broken time-reversal symmetry and its role in driving non-trivial topological phase transitions. By varying the spin-orbit coupling parameters, we find both a semimetal/insulator phase transition and a topological phase transition between insulating phases with a different number of edge states. The spin is not a conserved quantity of the system and the topological phase transitions can be detected by analyzing its polarization in time of flight images, providing a clear diagnostics for the characterization of the topological phases through the partial entanglement between spin and lattice degrees of freedom.</blockquote>View original: <a href="http://arxiv.org/abs/1308.0750">http://arxiv.org/abs/1308.0750</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-1230675232101180877.post-11688146441625728602013-08-06T00:01:00.011-07:002013-08-06T00:01:39.703-07:001308.0756 (Adrian E. Feiguin et al.)<h2 class="title"><a href="http://arxiv.org/abs/1308.0756">Hermitian and non-Hermitian thermal Hamiltonians</a> [<a href="http://arxiv.org/pdf/1308.0756">PDF</a>]</h2>Adrian E. Feiguin, Israel Klich<a name='more'></a><blockquote class="abstract">Thermal density matrices can be described by a pure quantum state within the thermofield formalism. Here we show how to construct a class of Hamiltonians realizing a thermofield state as their ground state. These Hamiltonians are frustration-free, and can be Hermitian or non-Hermitian, allowing one to use ground-state methods to understand the thermodynamic properties of the system. In particular this approach gives an explicit mapping of thermal phase transitions into quantum phase transitions. In the non-Hermitian case, the quantum phase transition is not accompanied by a change in the spectrum of the Hamiltonian, which remains gapped. We illustrate these ideas for the classical 2D Ising model.</blockquote>View original: <a href="http://arxiv.org/abs/1308.0756">http://arxiv.org/abs/1308.0756</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-1230675232101180877.post-36602739543843332402013-08-06T00:01:00.009-07:002013-08-06T00:01:38.732-07:001308.0793 (Michel Bauer et al.)<h2 class="title"><a href="http://arxiv.org/abs/1308.0793">Real time imaging of quantum and thermal fluctuations: the case of a<br /> two-level system</a> [<a href="http://arxiv.org/pdf/1308.0793">PDF</a>]</h2>Michel Bauer, Denis Bernard<a name='more'></a><blockquote class="abstract">A quantum system in contact with a heat bath undergoes quantum transitions between energy levels upon absorption or emission of energy quanta by the bath. These transitions remain virtual until the energy of the system is measured repeatedly, even continuously in time. Isolating the two indispensible mechanisms in competition, we describe in a synthetic way the main physical features of thermally activated quantum jumps. Using classical tools of stochastic analysis, we compute in the case of a Q-bit the complete statistics of jumps and transition times in the limit when the typical measurement time is small compared to the thermal relaxation time. The emerging picture is that quantum trajectories are similar to those of a classical particle in a noisy environment, subject to transitions a la Kramers in a multi well landscape, but with a large multiplicative noise.</blockquote>View original: <a href="http://arxiv.org/abs/1308.0793">http://arxiv.org/abs/1308.0793</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-1230675232101180877.post-4405699967127098842013-08-06T00:01:00.007-07:002013-08-06T00:01:37.780-07:001308.0823 (H. Schenck et al.)<h2 class="title"><a href="http://arxiv.org/abs/1308.0823">Vector chiral phases in frustrated 2D XY model and quantum spin chains</a> [<a href="http://arxiv.org/pdf/1308.0823">PDF</a>]</h2>H. Schenck, V. L. Pokrovsky, T. Nattermann<a name='more'></a><blockquote class="abstract">The phase diagram of the frustrated 2D XY model is calculated analytically. The chiral (Ising) transition is described by three independent critical exponents which are calculated in $d=5/2-\epsilon$ dimensions. Vortex interaction is short range on small and logarithmic on large scales, if compared with the chiral correlation length $\xi$. The vortex unbinding transitions is triggered by the increase of $\xi$ and occurs before the chiral transition takes place. In a narrow region close to the Lifshitz point a reentrant quasi-ferromagnetic phase appears. Application to antiferromagnetic quantum spin chains and multiferroics are discussed.</blockquote>View original: <a href="http://arxiv.org/abs/1308.0823">http://arxiv.org/abs/1308.0823</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-1230675232101180877.post-81140530887528757912013-08-06T00:01:00.005-07:002013-08-06T00:01:36.936-07:001308.0962 (Sona John et al.)<h2 class="title"><a href="http://arxiv.org/abs/1308.0962">Effect of linkage on the equilibrium frequency of deleterious mutations</a> [<a href="http://arxiv.org/pdf/1308.0962">PDF</a>]</h2>Sona John, Kavita Jain<a name='more'></a><blockquote class="abstract">We study the evolution of an asexual population of binary sequences of finite length in which both deleterious and reverse mutations can occur. Such a model has been used to understand the prevalence of preferred codons due to selection, mutation and drift, and proposed as a possible mechanism for halting the irreversible degeneration of asexual population due to Muller's ratchet. Using an analytical argument and numerical simulations, we study the dependence of the equilibrium fraction of deleterious mutations on various population genetic parameters. In contrast to the one-locus theory, where the fraction of disadvantageous mutations decreases exponentially fast with increasing population size, we find that in the multilocus model, it decreases to zero exponentially for very large populations but approaches a constant for smaller populations logarithmically. The weak dependence on the population size may explain the similar levels of codon bias seen in populations of different sizes.</blockquote>View original: <a href="http://arxiv.org/abs/1308.0962">http://arxiv.org/abs/1308.0962</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-1230675232101180877.post-81284571821527359312013-08-06T00:01:00.003-07:002013-08-06T00:01:35.797-07:001308.0972 (Jürg Diemand et al.)<h2 class="title"><a href="http://arxiv.org/abs/1308.0972">Large Scale Molecular Dynamics Simulations of Homogeneous Nucleation</a> [<a href="http://arxiv.org/pdf/1308.0972">PDF</a>]</h2>Jürg Diemand, Raymond Angélil, Kyoko K. Tanaka, Hidekazu Tanaka<a name='more'></a><blockquote class="abstract">We present results from large-scale molecular dynamics (MD) simulations of homogeneous vapor-to-liquid nucleation. The simulations contain between one and eight billion Lennard-Jones (LJ) atoms, covering up to 1.2 {\mu}s (56 million time-steps). They cover a wide range of supersaturation ratios, S=1.55 to 10^4, and temperatures from kT = 0.3 to 1.0 {\epsilon} (where {\epsilon} is the depth of the LJ potential, and k the Boltzmann constant). We have resolved nucleation rates as low as 10^{17} cm^{-3} s^{-1} (in the argon system), and critical cluster sizes as large as 100 atoms. Recent argon nucleation experiments probe nucleation rates in an overlapping range, making the first direct comparison between laboratory experiments and molecular dynamics simulations possible: We find very good agreement within the uncertainties, which are mainly due to the extrapolations of argon and LJ saturation curves to very low temperatures. The self-consistent, modified classical nucleation model of Girshick and Chiu [J. Chem. Phys. 93, 1273 (1990)] underestimates the nucleation rates by up to 9 orders of magnitudes at low temperatures, and at kT = 1.0 {\epsilon} it overestimates them by up to 10^5. The predictions from a semi-phenomenological model by Laaksonen et al. [Phys. Rev. E 49, 5517 (1994)] are much closer to our MD results, but still differ by factors of up to 104 in some cases. At low temperatures, the classical theory predicts critical clusters sizes, which match the simulation results (using the first nucleation theorem) quite well, while the semi-phenomenological model slightly underestimates them. At kT = 1.0 {\epsilon} the critical sizes from both models are clearly too small. (abridged)</blockquote>View original: <a href="http://arxiv.org/abs/1308.0972">http://arxiv.org/abs/1308.0972</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-1230675232101180877.post-33978280495580399222013-08-06T00:01:00.001-07:002013-08-06T00:01:34.719-07:001308.1083 (Eric Perlmutter)<h2 class="title"><a href="http://arxiv.org/abs/1308.1083">A universal feature of CFT Renyi entropy</a> [<a href="http://arxiv.org/pdf/1308.1083">PDF</a>]</h2>Eric Perlmutter<a name='more'></a><blockquote class="abstract">We show that for a d-dimensional CFT in flat space, the Renyi entropy S_q across a spherical entangling surface has the following property: in an expansion around q=1, the first correction to the entanglement entropy is proportional to C_T, the coefficient of the stress tensor vacuum two-point function, with a fixed d-dependent coefficient. This is equivalent to a similar statement about the free energy of CFTs living on S^1 x H^{d-1} with inverse temperature \beta=2\pi q. In addition to furnishing a direct argument applicable to all CFTs, we exhibit this result using a handful of gravity and field theory computations. Knowledge of C_T thus doubles as knowledge of Renyi entropies in the neighborhood of q=1, which we use to establish new results in 3d vector models at large N.</blockquote>View original: <a href="http://arxiv.org/abs/1308.1083">http://arxiv.org/abs/1308.1083</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-1230675232101180877.post-69932772054505983952013-08-05T00:01:00.005-07:002013-08-05T00:01:25.903-07:001308.0430 (Adam Nahum et al.)<h2 class="title"><a href="http://arxiv.org/abs/1308.0430">Length Distributions in Loop Soups</a> [<a href="http://arxiv.org/pdf/1308.0430">PDF</a>]</h2>Adam Nahum, J. T. Chalker, P. Serna, M. Ortuno, A. M. Somoza<a name='more'></a><blockquote class="abstract">Statistical lattice ensembles of loops in three or more dimensions typically have phases in which the longest loops fill a finite fraction of the system. In such phases it is natural to ask about the distribution of loop lengths. We show how to calculate moments of these distributions using $CP^{n-1}$ or $RP^{n-1}$ and O(n) $\sigma$ models together with replica techniques. The resulting joint length distribution for macroscopic loops is Poisson-Dirichlet with a parameter $\theta$ fixed by the loop fugacity and by symmetries of the ensemble. We also discuss features of the length distribution for shorter loops, and use numerical simulations to test and illustrate our conclusions.</blockquote>View original: <a href="http://arxiv.org/abs/1308.0430">http://arxiv.org/abs/1308.0430</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-1230675232101180877.post-74196508137076187932013-08-05T00:01:00.003-07:002013-08-05T00:01:24.809-07:001308.0491 (José A. Cuesta et al.)<h2 class="title"><a href="http://arxiv.org/abs/1308.0491">Time-shift invariance determines the functional shape of the current in<br /> rocking ratchets</a> [<a href="http://arxiv.org/pdf/1308.0491">PDF</a>]</h2>José A. Cuesta, Niurka R. Quintero, Renato Alvarez-Nodarse<a name='more'></a><blockquote class="abstract">Ratchets are devices able to rectify an otherwise oscillatory behavior by exploiting an asymmetry of the system. In rocking ratchets the asymmetry is induced through a proper choice of external forces and modulations of nonlinear symmetric potentials. The ratchet currents thus obtained in systems as different as semiconductors, Josephson junctions, optical lattices, or ferrofluids, show a set of universal features. A satisfactory explanation for them has challenged theorist for decades, and so far we still lack a general theory of this phenomenon. Here we provide such a theory by exploring ---through functional analysis--- the constraints that the simple assumption of time-shift invariance of the ratchet current imposes on its dependence on the external drivings. Because the derivation is based on so general a principle, the resulting expression is valid irrespective of the details and the nature of the physical systems to which it is applied, and of whether they are classical, quantum, or stochastic. The theory also explains deviations observed from universality under special conditions, and allows to make predictions of phenomena not yet observed in any experiment or simulation.</blockquote>View original: <a href="http://arxiv.org/abs/1308.0491">http://arxiv.org/abs/1308.0491</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-1230675232101180877.post-52969955976221606812013-08-05T00:01:00.001-07:002013-08-05T00:01:23.890-07:001308.0556 (Philip W Anderson)<h2 class="title"><a href="http://arxiv.org/abs/1308.0556">The Dilemma of Bose Solids: is He Supersolid?</a> [<a href="http://arxiv.org/pdf/1308.0556">PDF</a>]</h2>Philip W Anderson<a name='more'></a><blockquote class="abstract">Nearly a decade ago the old controversy about possible superfluid flow in the ground state of solid He4 was revived by the apparent experimental observation of such superflow. Although the experimentalists have recently retracted, very publicly, some of the observations on which such a claim was based, other confirming observations of which there is no reason for doubt remain on the record. Meanwhile theoretical arguments bolstered by some experimental evidence strongly favor the existence of supersolidity in the Bose-Hubbard model, and these arguments would seem to extend to solid He. The true situation thus is apparently extraordinarily opaque. The situation is complicated by the fact that all accurate simulation studies on Heuse the uniform sign hypothesis which confines them to the phase-coherent state, which is, in principle, supersolid, so that no accurate simulations of the true, classical solid exist. There is great confusion as to the nature of the ground state wave-function for a bose quantum solid, and we suggest that until that question is cleared up none of these dilemmas will be resolved.</blockquote>View original: <a href="http://arxiv.org/abs/1308.0556">http://arxiv.org/abs/1308.0556</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-1230675232101180877.post-70513386495110597672013-08-04T00:02:00.003-07:002013-08-04T00:02:03.645-07:000804.3153 (S. A. Alavi)<h2 class="title"><a href="http://arxiv.org/abs/0804.3153">Thermodynamics of quasianti-Hermitian quaternionic systems</a> [<a href="http://arxiv.org/pdf/0804.3153">PDF</a>]</h2>S. A. Alavi<a name='more'></a><blockquote class="abstract">Thermodynamics of quasianti-Hermitian quaternionic systems with constant number of particles in equilibrium is studied. A toy model is introduced and the physically relevant quantities are derived. The energy fluctuation which shows that for large N the relative r.m.s fluctuation in the values of E is quite negligible is derived. The negative temperature for such systems is also studied. Finally a physical example is discussed and physical explanations in the context of quantum physics are given.</blockquote>View original: <a href="http://arxiv.org/abs/0804.3153">http://arxiv.org/abs/0804.3153</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-1230675232101180877.post-17855959108765898772013-08-04T00:02:00.001-07:002013-08-04T00:02:00.639-07:001308.0034 (Shuai Shao et al.)<h2 class="title"><a href="http://arxiv.org/abs/1308.0034">Robustness of partially interdependent network formed of clustered<br /> networks</a> [<a href="http://arxiv.org/pdf/1308.0034">PDF</a>]</h2>Shuai Shao, Xuqing Huang, H. Eugene Stanley, Shlomo Havlin<a name='more'></a><blockquote class="abstract">Clustering, or transitivity has been observed in real networks and its effects on their structure and function has been discussed extensively. The focus of these studies has been on clustering of single networks while the effect of clustering on the robustness of coupled networks received very little attention. Only the case of a pair of fully coupled networks with clustering has been studied recently. Here we generalize the study of clustering of a fully coupled pair of networks to the study of partially interdependent network of networks with clustering within the network components. We show both analytically and numerically, how clustering within the networks, affects the percolation properties of interdependent networks, including percolation threshold, size of giant component and critical coupling point where first order phase transition changes to second order phase transition as the coupling between the networks reduces. We study two types of clustering: one type proposed by Newman where the average degree is kept constant while changing the clustering and the other proposed by Hackett $et$ $al.$ where the degree distribution is kept constant. The first type of clustering is treated both analytically and numerically while the second one is treated only numerically.</blockquote>View original: <a href="http://arxiv.org/abs/1308.0034">http://arxiv.org/abs/1308.0034</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-1230675232101180877.post-78614854105954996822013-08-04T00:01:00.011-07:002013-08-04T00:01:59.803-07:001308.0048 (Mikhail A. Anisimov)<h2 class="title"><a href="http://arxiv.org/abs/1308.0048">Fifty Years of Breakthrough Discoveries in Fluid Criticality</a> [<a href="http://arxiv.org/pdf/1308.0048">PDF</a>]</h2>Mikhail A. Anisimov<a name='more'></a><blockquote class="abstract">Fifty years ago two scientists, who celebrate their 80th birthdays in 2011, Alexander V. Voronel and Johannes V. Sengers performed breakthrough experiments that challenged the commonly accepted views on critical phenomena in fluids. Voronel discovered that the isochoric heat capacity of argon becomes infinite at the vapor-liquid critical point. Almost simultaneously, Sengers observed a similar anomaly for the thermal conductivity of near-critical carbon dioxide. The existence of these singularities was later proved to be universal for all fluids. These experiments had a profound effect on the development of the modern (scaling) theory of phase transitions, which is based on the diverging fluctuations of the order parameter. In particular, the discovery of the heat-capacity divergence at the critical point was a keystone for the formulation of static scaling theory, while the discovery of the divergence of the thermal conductivity played an important role in the formulation of dynamic scaling and mode-coupling theory. Moreover, owing to the discoveries made by Voronel and Sengers 50 years ago, critical phenomena in fluids have become an integral part of contemporary condensed-matter physics.</blockquote>View original: <a href="http://arxiv.org/abs/1308.0048">http://arxiv.org/abs/1308.0048</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-1230675232101180877.post-19254435952871713152013-08-04T00:01:00.009-07:002013-08-04T00:01:55.633-07:001308.0082 (Upendra Harbola et al.)<h2 class="title"><a href="http://arxiv.org/abs/1308.0082">Large deviation function and fluctuation theorem for classical particle<br /> transport</a> [<a href="http://arxiv.org/pdf/1308.0082">PDF</a>]</h2>Upendra Harbola, Christian Van den Broeck, Katja Lindenberg<a name='more'></a><blockquote class="abstract">We analytically evaluate the large deviation function in a simple model of classical particle transfer between two reservoirs. We illustrate how the asymptotic large time regime is reached starting from a special propagating initial condition. We show that the steady state fluctuation theorem holds provided that the distribution of the particle number decays faster than an exponential, implying analyticity of the generating function and a discrete spectrum for its evolution operator.</blockquote>View original: <a href="http://arxiv.org/abs/1308.0082">http://arxiv.org/abs/1308.0082</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-1230675232101180877.post-63380505237851416582013-08-04T00:01:00.007-07:002013-08-04T00:01:53.046-07:001308.0144 (Adam Nahum et al.)<h2 class="title"><a href="http://arxiv.org/abs/1308.0144">Phase transitions in 3D loop models and the $CP^{n-1}$ $σ$ model</a> [<a href="http://arxiv.org/pdf/1308.0144">PDF</a>]</h2>Adam Nahum, J. T. Chalker, P. Serna, M. Ortuno, A. M. Somoza<a name='more'></a><blockquote class="abstract">We consider the statistical mechanics of a class of models involving close-packed loops with fugacity $n$ on three-dimensional lattices. The models exhibit phases of two types as a coupling constant is varied: in one, all loops are finite, and in the other, some loops are infinitely extended. We show that the loop models are discretisations of $CP^{n-1}$ $\sigma$ models. The finite and infinite loop phases represent, respectively, disordered and ordered phases of the $\sigma$ model, and we discuss the relationship between loop properties and $\sigma$ model correlators. On large scales, loops are Brownian in an ordered phase and have a non-trivial fractal dimension at a critical point. We simulate the models, finding continuous transitions between the two phases for $n=1,2,3$ and first order transitions for $n\geq 4$. We also give a renormalisation group treatment of the $CP^{n-1}$ model that shows how a continuous transition can survive for values of $n$ larger than (but close to) two, despite the presence of a cubic invariant in the Landau-Ginzburg description. The results we obtain are of broader relevance to a variety of problems, including SU(n) quantum magnets in (2+1) dimensions, Anderson localisation in symmetry class C, and the statistics of random curves in three dimensions.</blockquote>View original: <a href="http://arxiv.org/abs/1308.0144">http://arxiv.org/abs/1308.0144</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-1230675232101180877.post-39772338134450620152013-08-04T00:01:00.005-07:002013-08-04T00:01:52.246-07:001308.0255 (Chung-Pin Chou et al.)<h2 class="title"><a href="http://arxiv.org/abs/1308.0255">Order-disorder duality of second order phase transitions: The topology<br /> of complex networks</a> [<a href="http://arxiv.org/pdf/1308.0255">PDF</a>]</h2>Chung-Pin Chou, Ming-Chiang Chung<a name='more'></a><blockquote class="abstract">Many networks of interests in the real world, such as social networks, computer networks and biological networks, have been widely studied by using network analysis tools. In this letter we use these techniques to study phase transitions in one-dimensional quantum Ising model and two-dimensional classical XY model. We demonstrate that whereas the phase in real space is transited from an ordered to a disordered state, the network topology surprisingly changes from a disordered to an ordered state. We call this correspondence as "order-disorder duality". Several network quantities, e.g., global efficiency, clustering coefficient and small-worldness, can play similar roles as order parameters in Landau symmetry-breaking theory. We suggest that the network measurements originating from topological network structures can provide useful tools to characterize the phase transitions in any given model. In addition, we discuss the possibility of the small-world property in these two models.</blockquote>View original: <a href="http://arxiv.org/abs/1308.0255">http://arxiv.org/abs/1308.0255</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-1230675232101180877.post-23828830383372218582013-08-04T00:01:00.003-07:002013-08-04T00:01:50.564-07:001308.0277 (Maurizio Fagotti)<h2 class="title"><a href="http://arxiv.org/abs/1308.0277">Dynamical Phase Transitions as Properties of the Stationary State:<br /> Analytic Results after Quantum Quenches in the Spin-1/2 XXZ Chain</a> [<a href="http://arxiv.org/pdf/1308.0277">PDF</a>]</h2>Maurizio Fagotti<a name='more'></a><blockquote class="abstract">The (Loschmidt) overlap between the state at different times after a quantum quench is attracting increasing interest, as it was recently shown to have a non-analytic behavior if a Hamiltonian parameter is quenched across a critical point. This phenomenon was called a "dynamical phase transition" in analogy with the behavior of the canonical partition function at an equilibrium phase transition. We consider the nonequilibrium time evolution with the Hamiltonian of the XXZ spin-1/2 chain and derive a general expression for the Loschmidt amplitude. We represent the state that describes the stationary properties of (local) observables as a Gibbs ensemble of a generalized Hamiltonian. By analyzing the large time behavior of the overlap, we reveal a deep connection between the appearance of singularities and the spectral properties of the generalized Hamiltonian.</blockquote>View original: <a href="http://arxiv.org/abs/1308.0277">http://arxiv.org/abs/1308.0277</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-1230675232101180877.post-76086752420857180592013-08-04T00:01:00.001-07:002013-08-04T00:01:49.721-07:001308.0284 (Shamik Gupta et al.)<h2 class="title"><a href="http://arxiv.org/abs/1308.0284">Anomalous dynamics of a tagged monomer of a long polymer chain: The case<br /> of harmonic pinning and harmonic absorption</a> [<a href="http://arxiv.org/pdf/1308.0284">PDF</a>]</h2>Shamik Gupta, Alberto Rosso, Christophe Texier<a name='more'></a><blockquote class="abstract">We study the anomalous dynamics of a tagged monomer of a Rouse polymer chain. In presence of harmonic pinning or harmonic absorption, an exact solution shows that a unique steady state is reached at long times. However, the initial configuration of the polymer strongly affects the approach to the steady state, that we explicitly compute for the one-dimensional case. Generalizations to higher dimensions and elastic interfaces are also discussed.</blockquote>View original: <a href="http://arxiv.org/abs/1308.0284">http://arxiv.org/abs/1308.0284</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-1230675232101180877.post-59900661926011170362013-08-02T00:45:00.001-07:002013-08-02T00:45:34.518-07:001307.8219 (Swathi S. Hegde et al.)<h2 class="title"><a href="http://arxiv.org/abs/1307.8219">Freezing a Quantum Magnet by Repeated Quantum Interference: An<br /> Experimental Realization</a> [<a href="http://arxiv.org/pdf/1307.8219">PDF</a>]</h2>Swathi S. Hegde, Hemant Katiyar, T. S. Mahesh, Arnab Das<a name='more'></a><blockquote class="abstract">We experimentally demonstrate the phenomenon of dynamical many-body freezing in a periodically driven quantum Ising magnet within an NMR simulation scheme. The phenomenon is essentially a result of repeated quantum interference between the amplitudes of the fundamental excitations of the many-body system. The degree of freezing exhibits surprising non-monotonic behavior with respect to the driving frequency. At the points of maximal freezing, the population dynamics of all the quasi-particle modes are frozen very strongly for all time, which renders the freezing occurring independent of initial state and visible for almost all system sizes. Magnetization measured for our finite spin system gives direct access to the time-evolution of the underlying fermionic excitations in momentum space.</blockquote>View original: <a href="http://arxiv.org/abs/1307.8219">http://arxiv.org/abs/1307.8219</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-1230675232101180877.post-4128969531304872812013-08-01T00:31:00.011-07:002013-08-01T00:31:27.951-07:001307.8117 (Brian Swingle)<h2 class="title"><a href="http://arxiv.org/abs/1307.8117">Entanglement does not generally decrease under renormalization</a> [<a href="http://arxiv.org/pdf/1307.8117">PDF</a>]</h2>Brian Swingle<a name='more'></a><blockquote class="abstract">Renormalization is often described as the removal or "integrating out" of high energy degrees of freedom. In the context of quantum matter, one might suspect that quantum entanglement provides a sharp way to characterize such a loss of degrees of freedom. Indeed, for quantum many-body systems with Lorentz invariance, such entanglement monotones have been proven to exist in one, two, and three spatial dimensions. In each dimension d, a certain term in the entanglement entropy of a d-ball decreases along renormalization group (RG) flows. Given that most quantum many-body systems available in the laboratory are not Lorentz invariant, it is important to generalize these results if possible. In this work we demonstrate the impossibility of a wide variety of such generalizations. We do this by exhibiting a series of counterexamples with understood renormalization group flows which violate entanglement RG monotonicity. We discuss bosons at finite density, fermions at finite density, and majorization in Lorentz invariant theories, among other results.</blockquote>View original: <a href="http://arxiv.org/abs/1307.8117">http://arxiv.org/abs/1307.8117</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-1230675232101180877.post-83766230599656830312013-08-01T00:31:00.009-07:002013-08-01T00:31:27.204-07:001307.8234 (Emilio N. M. Cirillo et al.)<h2 class="title"><a href="http://arxiv.org/abs/1307.8234">Effect of self-interaction on the phase diagram of a Gibbs-like measure<br /> derived by a reversible Probabilistic Cellular Automata</a> [<a href="http://arxiv.org/pdf/1307.8234">PDF</a>]</h2>Emilio N. M. Cirillo, P. -Y. Louis, W. M. Ruszel, C. Spitoni<a name='more'></a><blockquote class="abstract">Cellular Automata are discrete-time dynamical systems on a spatially extended discrete space which provide paradigmatic examples of nonlinear phenomena. Their stochastic generalizations, i.e., Probabilistic Cellular Automata (PCA), are discrete time Markov chains on lattice with finite single-cell states whose distinguishing feature is the \emph{parallel} character of the updating rule. We study the ground states of the Hamiltonian and the low-temperature phase diagram of the related Gibbs measure naturally associated with a class of reversible PCA, called the \textit{cross PCA}. In such a model the updating rule of a cell depends indeed only on the status of the five cells forming a cross centered at the original cell itself. In particular, it depends on the value of the center spin (\textit{self-interaction}). The goal of the paper is that of investigating the role played by the self-interaction parameter in connection with the ground states of the Hamiltonian and the low-temperature phase diagram of the Gibbs measure associated with this particular PCA.</blockquote>View original: <a href="http://arxiv.org/abs/1307.8234">http://arxiv.org/abs/1307.8234</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0tag:blogger.com,1999:blog-1230675232101180877.post-84980871772852098882013-08-01T00:31:00.007-07:002013-08-01T00:31:26.263-07:001307.8252 (Simone Pigolotti et al.)<h2 class="title"><a href="http://arxiv.org/abs/1307.8252">On the selective advantage of diffusing faster</a> [<a href="http://arxiv.org/pdf/1307.8252">PDF</a>]</h2>Simone Pigolotti, Roberto Benzi<a name='more'></a><blockquote class="abstract">We study a stochastic spatial model of biological competition in which two species have the same birth and death rates, but different diffusion constant. We show that even a relative difference in diffusivity on the order of a few percent may lead to a strong bias in the coarsening process favoring the more agile species. We quantify this selective advantage theoretically and present analytical formulas for the average growth of the fastest species and its fixation probability. Finally, we show that advection by an incompressible flow does not alter our result, provided the turbulent scale is sufficiently large, while introducing a compressible flow significantly dampens the effect.</blockquote>View original: <a href="http://arxiv.org/abs/1307.8252">http://arxiv.org/abs/1307.8252</a>C.P.R.http://www.blogger.com/profile/13598012384534951656noreply@blogger.com0