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

Dynamical phase transitions (DPTs) are nonequilibrium counterparts of thermodynamic phase transitions and share many similarities with their equilibrium analogs. In continuous phase transitions, critical exponents (CEs) play a key role in characterizing the physics near criticality. In this paper, we aim at systematically analyzing the set of possible CEs 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 CEs can be categorized into a limited set of distinct cases, suggesting a constrained universality in weak noise-induced DPTs. 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.