Systematic analysis of critical exponents in continuous dynamical phase transitions of weak noise theories

TL;DR

This paper systematically analyzes critical exponents in weak noise dynamical phase transitions in 1+1 dimensions, revealing limited universality classes through Gaussian fluctuation methods and illustrating with KPZ and exclusion process examples.

Contribution

It introduces a Gaussian fluctuation approach to classify critical exponents without Landau theory, uncovering constrained universality in weak noise dynamical phase transitions.

Findings

Critical exponents form a limited set of universality classes.

Gaussian fluctuation method effectively characterizes critical behavior.

Applications to KPZ and exclusion processes demonstrate the framework's utility.

Abstract

Dynamical phase transitions are nonequilibrium counterparts of thermodynamic phase transitions and share many similarities with their equilibrium analogs. In continuous phase transitions, critical exponents play a key role in characterizing the physics near criticality. This study aims to systematically analyze the set of possible critical exponents in weak noise statistical field theories in 1+1 dimensions, focusing on cases with a single fluctuating field. To achieve this, we develop and apply the Gaussian fluctuation method, avoiding reliance on constructing a Landau theory based on system symmetries. Our analysis reveals that the critical exponents can be categorized into a limited set of distinct cases, suggesting a constrained universality in weak noise-induced dynamical phase transitions. We illustrate our findings in two examples: short-time large deviations of the Kardar-Parisi-Zhang equation, and the weakly asymmetric exclusion process on a ring within the framework of the macroscopic fluctuation theory.