Dynamics of non-Gaussian fluctuations in model A

TL;DR

This study investigates the dynamic scaling behavior of non-Gaussian fluctuations in a model A stochastic field theory, revealing consistent critical exponents across moments and complex relaxation dynamics after quenches.

Contribution

It provides the first detailed analysis of higher moment correlation functions and their relaxation properties in model A near criticality.

Findings

Dynamic scaling with z=2.026(56) for correlation functions.

Same critical exponent z applies to higher moments of the order parameter.

Complex early and late stage relaxation behavior observed after quenches.

Abstract

Motivated by the experimental search for the QCD critical point we perform simulations of a stochastic field theory with purely relaxational dynamics (model A). We verify the expected dynamic scaling of correlation functions. Using a finite size scaling analysis we obtain the dynamic critical exponent $z=2.026(56)$. We investigate time dependent correlation functions of higher moments $M^n(t)$ of the order parameter $M(t)$ for $n=1,2,3,4$. We obtain dynamic scaling with the same critical exponent $z$ for all $n$, but the relaxation constant depends on $n$. We also study the relaxation of $M^n(t)$ after a quench, where the simulation is initialized in the high temperature phase, and the dynamics is studied at the critical temperature $T_c$. We find that the evolution does not follow simple scaling with the dynamic exponent $z$, and that it involves an early time rise followed by late stage relaxation.