Finite-Size Scaling of the Domain Wall Entropy Distributions for the 2D $\pm J$ Ising Spin Glass

TL;DR

This study investigates the finite-size scaling behavior of domain wall entropy distributions in the 2D ±J Ising spin glass, revealing different entropy characteristics depending on domain wall energy and lattice size.

Contribution

It provides a detailed analysis of how domain wall entropy distributions scale with system size and energy, highlighting differences between even and odd lattice sizes.

Findings

Entropy distribution for zero energy domain walls is approximately exponential.

Variance of entropy scales linearly with system size L.

Asymmetry and growth rate of entropy depend on domain wall energy.

Abstract

The statistics of domain walls for ground states of the 2D Ising spin glass with +1 and -1 bonds are studied for $L \times L$ square lattices with $L \le 48$, and $p$ = 0.5, where $p$ is the fraction of negative bonds, using periodic and/or antiperiodic boundary conditions. When $L$ is even, almost all domain walls have energy $E_{dw}$ = 0 or 4. When $L$ is odd, most domain walls have $E_{dw}$ = 2. The probability distribution of the entropy, $S_{dw}$, is found to depend strongly on $E_{dw}$. When $E_{dw} = 0$, the probability distribution of $|S_{dw}|$ is approximately exponential. The variance of this distribution is proportional to $L$, in agreement with the results of Saul and Kardar. For $E_{dw} = k > 0$ the distribution of $S_{dw}$ is not symmetric about zero. In these cases the variance still appears to be linear in $L$, but the average of $S_{dw}$ grows faster than $\sqrt{L}$. This suggests a one-parameter scaling form for the $L$-dependence of the distributions of $S_{dw}$ for $k > 0$.