Eigenmode analysis of the susceptibility matrix of the four-dimensional Edwards-Anderson spin-glass model

TL;DR

This study uses eigenmode analysis of the susceptibility matrix to investigate the spin-glass phase of the four-dimensional Edwards-Anderson model, revealing multiple extensive eigenvalues and anomalous temperature sensitivity.

Contribution

It provides new numerical evidence supporting replica-symmetry-breaking scenarios and introduces a dual formulation for efficient eigenmode analysis of large lattices.

Findings

Existence of multiple extensive eigenvalues in large lattices.

Eigenmodes show anomalous sensitivity to temperature changes.

Dual formulation offers computational advantages for large-scale analysis.

Abstract

The nature of spin-glass phase of the four-dimensional Edwards-Anderson Ising model is numerically studied by eigenmode analysis of the susceptibility matrix up to the lattice size 10^4. Unlike the preceding results on smaller lattices, our result suggests that there exist multiple extensive eigenvalues of the matrix, which does not contradict replica-symmetry-breaking scenarios. The sensitivity of the eigenmodes with respect to a temperature change is examined using finite-size-scaling analysis and an evidence of anomalous sensitivity is found. A computational advantage of dual formulation of the eigenmode analysis in the study of large lattices is also discussed.