Noisy Classical Field Theories with Two Coupled Fields: Dependence of Escape Rates on Relative Field Stiffnesses

TL;DR

This paper investigates how the escape rates in noisy classical field theories with two coupled fields depend on parameters like interval length, potential, and especially the relative stiffness of the fields, revealing a phase transition and critical slowing down.

Contribution

It provides the first comprehensive analysis of how varying relative field stiffnesses affects escape times in coupled classical field theories.

Findings

Escape rates depend on field stiffnesses and exhibit a phase transition.

A critical slowing down occurs near the transition point.

The study maps the complete phase diagram of escape times.

Abstract

Exit times for stochastic Ginzburg-Landau classical field theories with two or more coupled classical fields depend on the interval length on which the fields are defined, the potential in which the fields deterministically evolve, and the relative stiffness of the fields themselves. The latter is of particular importance in that physical applications will generally require different relative stiffnesses, but the effect of varying field stiffnesses has not heretofore been studied. In this paper, we explore the complete phase diagram of escape times as they depend on the various problem parameters. In addition to finding a transition in escape rates as the relative stiffness varies, we also observe a critical slowing down of the string method algorithm as criticality is approached.