Investigations into the characteristics and influences of nonequilibrium evolution

TL;DR

This study uses a 3D Ising model to analyze nonequilibrium evolution in relativistic heavy ion collisions, revealing how order parameters relax and how cumulants behave near the critical point, aiding experimental phase boundary determination.

Contribution

It demonstrates the exponential approach of order parameters to equilibrium and characterizes relaxation times, especially their divergence at critical temperature, providing insights into nonequilibrium dynamics.

Findings

Order parameter approaches equilibrium exponentially.

Relaxation time diverges at critical temperature as system size increases.

Cumulants of order parameter can be positive or negative depending on observation time.

Abstract

In order to estimate qualitatively the influence of nonequilibrium evolution in relativistic heavy ion collisions, we use the three dimensional Ising model with Metropolis algorithm to study the evolution from nonequilibrium to equilibrium on the phase boundary. The evolution of order parameter approaches its equilibrium value exponentially, the same as that given by Langevin equation. The average relaxation time is defined which is demonstrated to well represent the relaxation time in dynamical equations. It is shown that the average relaxation time at critical temperature diverges as the zth power of system size. The third and the fourth cumulants of order parameter during the nonequilibrium evolution could be either positive or negative, depending on the observation time, consistent with dynamical models at T > Tc. It is found that the nonequilibrium evolution at T > Tc lasts very short, and the influence is weaker than that at T < Tc. Those qualitative features are instructive to determine experimentally the critical point and the phase boundary of QCD.