Dynamics of non-Gaussian fluctuations in model A

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 T₂. 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.