Tree Approximation for Spin Glass Models

TL;DR

This paper introduces a tree-based approximation method for spin glass models that effectively captures sample-specific features and reproduces key qualitative behaviors observed in Monte Carlo simulations, providing a new computational approach.

Contribution

The paper presents a novel tree approximation technique for spin glass models that accurately reflects sample characteristics and aligns with known simulation results.

Findings

Successfully estimates critical temperature Tc ~ 1.0

Reproduces qualitative features of sample averages

Yields trivial overlap distribution function

Abstract

An approximate numerical approach to spin models is proposed, in which the original lattice is transformed into a tree. This method is applied to the Edwards-Anderson spin glass model in two and three dimensions. It captures the characteristics of each individual sample and reproduces various qualitative features of sample averaged quantities similar to those that have been observed in previous Monte Carlo simulations. For example, from the Binder parameter for various system sizes as a function of the temperature we obtain Tc ~ 1.0 with \nu ~ 1.85, in reasonable agreement with previous Monte Carlo simulations. The present approximation yields the trivial structure for the overlap distribution function.