Zero-Temperature Limit of the SUSY-breaking Complexity in Diluted Spin-Glass Models

TL;DR

This paper investigates the zero-temperature behavior of SUSY-breaking complexity in diluted spin-glass models, revealing concentration phenomena in field distributions for different coupling distributions.

Contribution

It provides new insights into the zero-temperature limit of SUSY-breaking complexity in Bethe lattice spin-glasses with various coupling distributions.

Findings

Fields concentrate on integers at low temperatures for bimodal couplings

SUSY-breaking and unbroken SUSY theories differ in field distribution behavior

Results hold for both quenched and annealed formulations

Abstract

We study the SUSY-breaking complexity of the Bethe Lattice Spin-Glass in the zero temperature limit. We consider both the Gaussian and the bimodal distribution of the coupling constants. For $J_{ij}=\pm 1$ the SUSY breaking theory yields fields distributions that concentrate on integer values at low temperatures, at variance with the unbroken SUSY theory. This concentration takes place both in the quenched as well as in the simpler annealed formulation.