Metastable States in Spin Glasses and Disordered Ferromagnets

TL;DR

This paper analytically investigates the properties and structure of metastable states in disordered Ising models, revealing their characteristics and overlaps through a dynamical approach applicable across all dimensions and M values.

Contribution

It introduces a dynamical method to analyze M-spin-flip stable states in disordered models, providing new insights into their number, energy, overlaps, and magnetizations.

Findings

Overlap distribution is a delta-function at zero.

Metastable states' energies and basins of attraction characterized.

A new dynamics for M=infinity offers a tool for ground state analysis.

Abstract

We study analytically M-spin-flip stable states in disordered short-ranged Ising models (spin glasses and ferromagnets) in all dimensions and for all M. Our approach is primarily dynamical and is based on the convergence of a zero-temperature dynamical process with flips of lattice animals up to size M and starting from a deep quench, to a metastable limit. The results (rigorous and nonrigorous, in infinite and finite volumes) concern many aspects of metastable states: their numbers, basins of attraction, energy densities, overlaps, remanent magnetizations and relations to thermodynamic states. For example, we show that their overlap distribution is a delta-function at zero. We also define a dynamics for M=infinity, which provides a potential tool for investigating ground state structure.