Numerical study of the overlap Lee-Yang singularities in the three-dimensional Edwards-Anderson model

TL;DR

This study numerically analyzes Lee-Yang zeros in the 3D Edwards-Anderson spin glass model, providing insights into phase transitions and the order parameter across different temperature regimes.

Contribution

It offers a detailed numerical characterization of Lee-Yang singularities in the 3D spin glass, including precise measurements of the anomalous dimension and phase transition properties.

Findings

Accurate measurement of the anomalous dimension at the critical point.

Characterization of the phase transition via the density of zeros.

Confirmation of the Edwards-Anderson order parameter values.

Abstract

We have characterized numerically, using the Janus computer, the Lee-Yang complex singularities related to the overlap in the 3D Ising spin glass with binary couplings in a wide range of temperatures (both in the critical and in the spin-glass phase). Studying the behavior of the zeros at the critical point, we have obtained an accurate measurement of the anomalous dimension in very good agreement with the values quoted in the literature. In addition, by studying the density of the zeros we have been able to characterize the phase transition and to investigate the Edwards-Anderson order parameter in the spin-glass phase, finding agreement with the values obtained using more conventional techniques.