Phase space geometry and slow dynamics

TL;DR

This paper introduces a high-dimensional phase space geometry mechanism that explains slow dynamics in spin-glass models and ferromagnetic domain growth, providing insights into ergodicity and quasi-equilibrium regimes.

Contribution

It reveals a non-Arrhenius slowing mechanism rooted in phase space geometry, applicable to spin-glass and ferromagnetic systems, advancing understanding of out-of-equilibrium dynamics.

Findings

Identifies a phase space geometry mechanism for slow dynamics.

Shows this mechanism applies to spin-glass and ferromagnetic models.

Provides a framework for understanding ergodicity and quasi-equilibrium states.

Abstract

We describe a non-Arrhenius mechanism for slowing down of dynamics that is inherent to the high dimensionality of the phase space. We show that such a mechanism is at work both in a family of mean-field spin-glass models without any domain structure and in the case of ferromagnetic domain growth. The marginality of spin-glass dynamics, as well as the existence of a `quasi equilibrium regime' can be understood within this scenario. We discuss the question of ergodicity in an out-of equilibrium situation.