The Eigenvalue Analysis of the Density Matrix of 4D Spin Glasses Supports Replica Symmetry Breaking

TL;DR

This paper introduces a numerical method to analyze the density matrix of spin glasses, applying it to 4D models, and provides evidence supporting replica symmetry breaking in the thermodynamic limit.

Contribution

The paper develops a general numerical approach for studying the density matrix of spin models and applies it to 4D spin glasses, demonstrating replica symmetry breaking.

Findings

Numerical method effectively analyzes density matrices of spin glasses.

Results support the existence of replica symmetry breaking in 4D spin glasses.

Findings contribute to understanding the phase structure of spin glasses.

Abstract

We present a general and powerful numerical method useful to study the density matrix of spin models. We apply the method to finite dimensional spin glasses, and we analyze in detail the four dimensional Edwards-Anderson model with Gaussian quenched random couplings. Our results clearly support the existence of replica symmetry breaking in the thermodynamical limit.