Fractal dimension of domain walls in the Edwards-Anderson spin glass model

TL;DR

This paper investigates the fractal dimension of domain walls in the Edwards-Anderson spin glass model, revealing distribution-dependent differences in two dimensions and contrasting behaviors with Schramm-Loewner evolution.

Contribution

It provides the first direct calculation of the fractal dimension of domain walls for bimodal and Gaussian distributions in the EA model, highlighting distribution effects in 2D.

Findings

In 3D, fractal dimension is the same for both distributions.

In 2D, fractal dimensions differ between distributions.

No evidence of Schramm-Loewner evolution for bimodal distribution in 2D.

Abstract

We study directly the length of the domain walls (DW) obtained by comparing the ground states of the Edwards-Anderson spin glass model subject to periodic and antiperiodic boundary conditions. For the bimodal and Gaussian bond distributions, we have isolated the DW and have calculated directly its fractal dimension $d_f$. Our results show that, even though in three dimensions $d_f$ is the same for both distributions of bonds, this is clearly not the case for two-dimensional (2D) systems. In addition, contrary to what happens in the case of the 2D Edwards-Anderson spin glass with Gaussian distribution of bonds, we find no evidence that the DW for the bimodal distribution of bonds can be described as a Schramm-Loewner evolution processes.