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

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.