1202.1658 (M. N. Najafi et al.)

Avalanche frontiers in dissipative abelian sandpile model as
off-critical SLE(2)    [PDF]

M. N. Najafi, Saman Moghimi-Araghi, S. Rouhani

Avalanche frontiers in Abelian Sandpile Model (ASM) are random simple curves
whose continuum limit is known to be a Schramm-Loewner Evolution (SLE) with
diffusivity parameter $\kappa = 2$. In this paper we consider the dissipative
ASM and study the statistics of the avalanche and wave frontiers for various
rates of dissipation. We examine the scaling behavior of a number of functions
such as the correlation length, the exponent of distribution function of loop
lengths and gyration radius defined for waves and avalanches. We find that they
do scale with the rate of dissipation. Two significant length scales are
observed. For length scales much smaller than the correlation length, these
curves show properties close to the critical curves and the corresponding
diffusivity parameter is nearly the same as the critical limit. We interpret
this as the ultra violet (UV) limit where $\kappa = 2$ corresponding to $c=-2$.
For length scales much larger than the correlation length we find that the
avalanche frontiers tend to Self-Avoiding Walk, the corresponding driving
function is proportional to the Brownian motion with the diffusion parameter
$\kappa =8/3$ corresponding to a field theory with $c = 0$. This is the infra
red (IR) limit. Correspondingly the central charge decreases from the IR to the
UV point.

View original: http://arxiv.org/abs/1202.1658