The role of symmetry in the short-time critical dymamics

TL;DR

This paper introduces a symmetry-based method to determine the short-time critical exponent in stochastic models, simplifying initial conditions and extending applicability to models with absorbing states.

Contribution

It presents a novel symmetry-based approach to calculate the short-time critical exponent using time correlation, reducing initial state constraints and broadening model coverage.

Findings

The method accurately determines the critical exponent from uncorrelated initial states.

It extends to models with absorbing states.

The approach simplifies the analysis of short-time critical dynamics.

Abstract

We show that the short-time critical exponent $\theta$ related to the critical initial slip in a stochastic model can be determined by the time correlation of the order parameter. In our procedure it suffices to start with an uncorrelated state with zero order parameter instead of departing, as usually done, from an initial state with a nonzero order parameter. The proof uses the group of symmetry operations related to the Markovian dynamics. Our scheme is extended to cover models with absorbing states.