Replica analysis of partition-function zeros in spin-glass models

TL;DR

This paper uses the replica method to analyze the distribution of partition-function zeros in mean-field spin-glass models, revealing phase diagrams and novel order parameters that characterize different zero distributions.

Contribution

It introduces a replica-based approach to locate partition-function zeros and uncovers new phase structures and order parameters in spin-glass models.

Findings

Identified two types of zero distributions: 2D within phases and 1D on phase boundaries.

Mapped the phase diagram of the random energy model in the complex parameter plane.

Proposed a new order parameter for phases with 2D zero distribution.

Abstract

We study the partition-function zeros in mean-field spin-glass models. We show that the replica method is useful to find the locations of zeros in a complex parameter plane. For the random energy model, we obtain the phase diagram in the plane and find that there are two types of distribution of zeros: two-dimensional distribution within a phase and one-dimensional one on a phase boundary. Phases with a two-dimensional distribution are characterized by a novel order parameter defined in the present replica analysis. We also discuss possible patterns of distributions by studying several systems.