Finite-size scaling of the Domain Wall Entropy for the 2D \pm J Ising Spin Glass

TL;DR

This study investigates the finite-size scaling of domain wall entropy in the 2D J Ising spin glass, revealing distinct behaviors based on domain wall energy and confirming some theoretical predictions while challenging others.

Contribution

It provides a detailed analysis of domain wall entropy distributions for different energies, confirming droplet model predictions for E_{dw} = 4 and clarifying discrepancies for E_{dw} = 0.

Findings

S_{dw} distributions agree with droplet model for E_{dw} = 4

S_{dw} for E_{dw} = 0 are non-Gaussian and match Saul and Kardar's results

Discrepancies with previous predictions are explained

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 $L \le 20$, and $x$ = 0.25 and 0.5, where $x$ is the fraction of negative bonds, using periodic and/or antiperiodic boundary conditions. Under these conditions, almost all domain walls have an energy $E_{dw}$ equal to 0 or 4. The probability distribution of the entropy, $S_{dw}$, is found to depend strongly on $E_{dw}$. The results for $S_{dw}$ when $E_{dw} = 4$ agree with the prediction of the droplet model. Our results for $S_{dw}$ when $E_{dw} = 0$ agree with those of Saul and Kardar. In addition, we find that the distributions do not appear to be Gaussian in that case. The special role of $E_{dw} = 0$ domain walls is discussed, and the discrepancy between the prediction of Amoruso, Hartmann, Hastings and Moore and the result of Saul and Kardar is explained.