Distribution of partition function zeros of the $\pm J$ model on the Bethe lattice

TL;DR

This paper investigates the distribution of partition function zeros in the $\

Contribution

It introduces a novel relation between cavity fields and zeros distribution, linking spin glass transitions to zeros in the thermodynamic limit.

Findings

Density of zeros matches phase boundaries

Spin glass transition characterized by zeros distribution

Continuous singularities touch real axes in spin glass phase

Abstract

The distribution of partition function zeros is studied for the $\pm J$ model of spin glasses on the Bethe lattice. We find a relation between the distribution of complex cavity fields and the density of zeros, which enables us to obtain the density of zeros for the infinite system size by using the cavity method. The phase boundaries thus derived from the location of the zeros are consistent with the results of direct analytical calculations. This is the first example in which the spin glass transition is related to the distribution of zeros directly in the thermodynamical limit. We clarify how the spin glass transition is characterized by the zeros of the partition function. It is also shown that in the spin glass phase a continuous distribution of singularities touches the axes of real field and temperature.