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

Abstract

We directly study the length of the domain walls (DWs) obtained by comparing the ground states of the Edwards-Anderson spin glass model subject to periodic and antiperiodic boundary conditions. For the bimodal and the Gaussian bond distributions, we have isolated the DW and have directly calculated 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 the Gaussian distribution of bonds, we find no evidence that the DW for the bimodal distribution of bonds can be described as Schramm-Loewner evolution processes.