Domain-Wall Free-Energy of Spin Glass Models:Numerical Method and Boundary Conditions

TL;DR

This paper introduces an extended Monte Carlo method to directly evaluate domain-wall free-energy in spin-glass models, providing new insights into phase transition characteristics and domain wall properties in 4d systems.

Contribution

The paper develops a novel Monte Carlo approach for direct domain-wall free-energy calculation and applies it to 4d spin glasses, obtaining critical parameters and domain wall exponents.

Findings

Critical temperature and exponents agree with previous studies.

The fractal dimension of domain walls indicates they are rough in the 4d phase.

The method provides a new tool for analyzing spin-glass phase transitions.

Abstract

An efficient Monte Carlo method is extended to evaluate directly domain-wall free-energy for randomly frustrated spin systems. Using the method, critical phenomena of spin-glass phase transition is investigated in 4d +/-J Ising model under the replica boundary condition. Our values of the critical temperature and exponent, obtained by finite-size scaling, are in good agreement with those of the standard MC and the series expansion studies. In addition, two exponents, the stiffness exponent and the fractal dimension of the domain wall, which characterize the ordered phase, are obtained. The latter value is larger than d-1, indicating that the domain wall is really rough in the 4d Ising spin glass phase.