Numerical Study of TAP Metastable States in 3-body Ising Spin Glasses

TL;DR

This paper numerically investigates the distribution of solutions to the TAP equations in 3-body Ising spin glasses, confirming theoretical predictions about BRST symmetry breaking and solution behavior across free energy levels.

Contribution

It provides a numerical validation of theoretical predictions regarding TAP solution distributions and BRST symmetry breaking in 3-body Ising spin glasses.

Findings

Qualitative reproduction of predicted macroscopic variable behavior.

Confirmation of BRST symmetry breaking at higher free energies.

Support for one-step replica symmetry breaking in the model.

Abstract

The distribution of solutions of the Thouless-Anderson-Palmer equation is studied by extensive numerical experiments for fully connected 3-body interaction Ising spin glass models in a level of annealed calculation. A recent study predicted that when the equilibrium state of the system is characterized by one-step replica symmetry breaking, the distribution is described by a Becchi-Rouet-Stora-Tyutin (BRST) supersymmetric solution in the relatively low free energy region, whereas the BRST supersymmetry is broken for higher values of free energy (Crisanti et al., Phys. Rev. B 71 (2005) 094202). Our experiments qualitatively reproduce the discriminative behavior of macroscopic variables predicted by the theoretical assessment.