Fractal dimension of spin glasses interfaces in dimensions $d=2$ and $d=3$ via strong disorder renormalization at zero temperature

TL;DR

This paper introduces a strong disorder renormalization method at zero temperature to analyze the fractal nature of domain walls in 2D and 3D Gaussian spin glasses, providing numerical estimates of their fractal dimensions.

Contribution

It presents a novel renormalization approach for spin glasses and quantifies the fractal dimensions of domain walls in low-dimensional systems.

Findings

Fractal dimension in 2D is approximately 1.27.

Fractal dimension in 3D is approximately 2.55.

Method applicable to large system sizes up to 2048^2 in 2D and 128^3 in 3D.

Abstract

For Gaussian Spin Glasses in low dimensions, we introduce a simple Strong Disorder renormalization procedure at zero temperature. In each disordered sample, the difference between the ground states associated to Periodic and Anti-Periodic boundary conditions defines a system-size Domain Wall. The numerical study in dimensions $d=2$ (up to sizes $2048^2$) and $d=3$ (up to sizes $128^3$) yields fractal Domain Walls of dimensions $d_s(d=2) \simeq 1.27$ and $d_s(d=3) \simeq 2.55$ respectively.