Nonperturbative fluctuations and metastability in a simple model: from observables to microscopic theory and back

TL;DR

This paper investigates how nonperturbative fluctuations influence metastability and phase transitions in a simple one-dimensional $\

Contribution

It introduces a detailed analysis of nonperturbative fluctuations in a toy model using finite size effects and nonperturbative Renormalization Group methods.

Findings

Nonperturbative fluctuations can destroy mean-field phase transitions.

Finite size and infrared cutoff methods lead to nonconvex effective potentials.

The study provides insights into treating strong nonperturbative effects.

Abstract

Slow dynamics in glassy systems is often interpreted as due to thermally activated events between "metastable" states. This emphasizes the role of nonperturbative fluctuations, which is especially dramatic when these fluctuations destroy a putative phase transition predicted at the mean-field level. To gain insight into such hard problems, we consider the implementation of a generic back-and-forth process, between microscopic theory and observable behavior via effective theories, in a toy model that is simple enough to allow for a thorough investigation: the one-dimensional $\varphi^4$ theory at low temperature. We consider two ways of restricting the extent of the fluctuations, which both lead to a nonconvex effective potential (or free energy) : either through a finite-size system or by means of a running infrared cutoff within the nonperturbative Renormalization Group formalism. We discuss the physical insight one can get and the ways to treat strongly nonperturbative fluctuations in this context.