Novel order parameter to describe the critical behavior of Ising spin glass models

TL;DR

This paper introduces a new order parameter $\\Phi$ for spin glasses, based on topology, which clarifies the phase transition and low-temperature phase in the Edwards-Anderson model, offering advantages over traditional measures.

Contribution

A new topologically-based order parameter $\\Phi$ is proposed and validated for spin glasses, providing clearer physical insights and improved analysis of phase transitions.

Findings

$\\Phi$ confirms a zero-temperature phase transition.

$\\Phi$ effectively identifies the low-temperature phase.

Finite size scaling supports the robustness of $\\Phi$.

Abstract

A novel order parameter $\Phi$ for spin glasses is defined based on topological criteria and with a clear physical interpretation. $\Phi$ is first investigated for well known magnetic systems and then applied to the Edwards-Anderson $\pm J$ model on a square lattice, comparing its properties with the usual $q$ order parameter. Finite size scaling procedures are performed. Results and analyses based on $\Phi$ confirm a zero temperature phase transition and allow to identify the low temperature phase. The advantages of $\Phi$ are brought out and its physical meaning is established.