Local state space geometry and thermal metastability in complex landscapes: the spin-glass case

TL;DR

This paper explores the geometry of configuration space in spin glasses, linking local minima structure to thermal stability and dynamics, revealing that metastability arises from the exponential density of states within energy traps.

Contribution

It introduces a geometric characterization of local minima neighborhoods in spin glasses and connects this to thermal metastability and dynamics through a combined analysis.

Findings

Configuration space neighborhoods of minima are hierarchically organized.

Thermal metastability is related to the exponential local density of states.

The model links real and configuration space descriptions of dynamics.

Abstract

A simple geometrical characterization of configuration space neighborhoods of local energy minima in spin glass landscapes is found by exhaustive search. Combined with previous Monte Carlo investigations of thermal domain growth, it allows a discussion of the connection between real and configuration space descriptions of low temperature relaxational dynamics. We argue that the part of state-space corresponding to a single growing domain is adequately modeled by a hierarchically organized set of states and that thermal (meta)stability in spin glasses is related to the nearly exponential local density of states present within each trap.