Zeros of the partition function and dynamical singularities in spin-glass systems

TL;DR

This paper investigates the distribution of partition function zeros in spin-glass systems using Lee-Yang theory and replica methods, revealing unique chaotic features and phase distinctions in complex parameter spaces.

Contribution

It introduces a novel analysis of zeros distribution in spin-glass models, highlighting differences between chaos and replica symmetry breaking.

Findings

Zeros form two-dimensional distributions in complex planes.

Chaotic phases at imaginary temperatures differ from traditional spin-glass phases.

Quantum dynamics can access the chaotic phase via quenching protocols.

Abstract

We study spin-glass systems characterized by continuous occurrence of singularities. The theory of Lee-Yang zeros is used to find the singularities. By using the replica method in mean-field systems, we show that two-dimensional distributions of zeros of the partition function in a complex parameter plane are characteristic feature of random systems. The results of several models indicate that the concept of chaos in the spin-glass state is different from that of the replica symmetry breaking. We discuss that a chaotic phase at imaginary temperature is different from the spin-glass phase and is accessible by quantum dynamics in a quenching protocol.