Ground-state energy and entropy of the two-dimensional Edwards-Anderson spin-glass model with different bond distributions

TL;DR

This paper employs advanced Monte Carlo and thermodynamic integration methods to accurately determine the ground-state energy and entropy of the 2D Edwards-Anderson spin-glass model across various bond distributions, extrapolating to the thermodynamic limit.

Contribution

It introduces a combined approach using parallel tempering and high-temperature expansion to precisely compute ground-state properties of the 2D spin-glass model for different bond types.

Findings

Accurate ground-state energy values for finite-size lattices.

Precise entropy estimates via thermodynamic integration.

Extrapolated thermodynamic limit results for different bond distributions.

Abstract

We study the two-dimensional Edwards-Anderson spin-glass model using a parallel tempering Monte Carlo algorithm. The ground-state energy and entropy are calculated for different bond distributions. In particular, the entropy is obtained by using a thermodynamic integration technique and an appropriate reference state, which is determined with the method of high-temperature expansion. This strategy provide accurate values of this quantity for finite-size lattices. By extrapolating to the thermodynamic limit, the ground-state energy and entropy of the different versions of the spin-glass model are determined.