1211.3675 (Y. Meurice)

Accurate exponents from approximate tensor renormalizations    [PDF]

Y. Meurice

Using two-state truncations of the Tensor Renormalization Group formulation of classical lattice models, we propose approximate recursion formulas for classical Ising models. In two spatial dimensions, we consider the cases of an isotropic blocking (as in the Migdal recursion) and an anisotropic blocking (as in the Kadanoff version) with two state projections based on a higher order singular value decomposition used in recent accurate numerical calculations by Tao Xiang's group. We propose a new type of accurate projection based on a transfer matrix. The transformations can be expressed as maps with 3 and 4 parameters in the isotropic and anisotropic cases respectively. Linear analysis near the nontrivial fixed point yields nu=0.987, 0.964 and 0.993 for the three maps respectively, which is much closer to the exact value 1 than 1.338 obtained in the Migdal and Kadanoff approximations. We discuss possible applications for the 3D Ising model and models with lattice fermions.

View original: http://arxiv.org/abs/1211.3675