Partition-function zeros of spherical spin glasses and their relevance to chaos

TL;DR

This paper studies the distribution of partition-function zeros in spherical spin glasses, revealing their connection to chaos effects and extending the replica method to complex temperatures.

Contribution

It extends the replica symmetry breaking approach to complex temperatures and links the density of zeros to chaos phenomena in spin glasses.

Findings

High density of zeros near the imaginary axis in the replica symmetric phase

No zeros density in spin-glass phases without chaos

Finite zeros density in spin-glass phases with chaos

Abstract

We investigate partition-function zeros of the many-body interacting spherical spin glass, the so-called $p$-spin spherical model, with respect to the complex temperature in the thermodynamic limit. We use the replica method and extend the procedure of the replica symmetry breaking ansatz to be applicable in the complex-parameter case. We derive the phase diagrams in the complex-temperature plane and calculate the density of zeros in each phase. Near the imaginary axis away from the origin, there is a replica symmetric phase having a large density. On the other hand, we observe no density in the spin-glass phases, irrespective of the replica symmetry breaking. We speculate that this suggests the absence of the temperature chaos. To confirm this, we investigate the multiple many-body interacting case which is known to exhibit the chaos effect. The result shows that the density of zeros actually takes finite values in the spin-glass phase, even on the real axis. These observations indicate that the density of zeros is more closely connected to the chaos effect than the replica symmetry breaking.