Dynamics of non-Gaussian fluctuations in model A
Thomas Schäfer, Vladimir V. Skokov
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.