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

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.

23 pages, 12 figures; minor changes

References in corpus (5)

• Quantum fluctuations in the transverse Ising spin glass model: A field theory of random quantum spin systems
• Distribution of Lee-Yang zeros and Griffiths singularities in the $\pm J$ model of spin glasses
• Replica symmetry breaking, complexity and spin representation in the generalized random energy model
• Spherical spin-glass - Coulomb gas duality: solution beyond mean-field theory
• Distribution of partition function zeros of the $\pm J$ model on the Bethe lattice

Cited by in corpus (3)

• Dynamical Singularities of Glassy Systems in a Quantum Quench
• Complex Random Energy Model: Zeros and Fluctuations
• Zeros of the partition function and dynamical singularities in spin-glass systems