The stiffness exponent of two-dimensional Ising spin glasses for non-periodic boundary conditions using aspect-ratio scaling

TL;DR

This paper investigates the scaling behavior of domain-wall energies in two-dimensional Ising spin glasses with different interaction distributions and boundary conditions, finding a boundary-condition-independent stiffness exponent for Gaussian interactions.

Contribution

It introduces an aspect-ratio scaling method to determine the stiffness exponent in 2D Ising spin glasses, revealing boundary-condition independence for Gaussian interactions.

Findings

Stiffness exponent theta = -0.287(4) for Gaussian interactions.

Aspect-ratio scaling confirms the predicted domain-wall energy behavior.

Method does not apply to bimodal interaction distributions.

Abstract

We study the scaling behavior of domain-wall energies in two-dimensional Ising spin glasses with Gaussian and bimodal distributions of the interactions and different types of boundary conditions. The domain walls are generated by changing the boundary conditions at T=0 in one direction. The ground states of the original and perturbed system are calculated numerically by applying an efficient matching algorithm. Systems of size LxM with different aspect-ratios 1/8 <= L/M <= 64 are considered. For Gaussian interactions, using the aspect-ratio scaling approach, we find a stiffness exponent theta=-0.287(4), which is independent of the boundary conditions in contrast to earlier results. Furthermore, we find a scaling behavior of the domain-wall energy as predicted by the aspect-ratio approach. Finally, we show that this approach does not work for the bimodal distribution of interactions.