Short-time critical dynamics

TL;DR

This paper reviews short-time critical dynamics, highlighting how early-stage power law behaviors enable the measurement of critical exponents and the distinction between first- and second-order phase transitions through numerical simulations.

Contribution

It introduces a method to analyze critical phenomena in the early evolution stage, reducing finite size effects and critical slowing down, for identifying phase transition types.

Findings

Power law behavior in early evolution stages allows critical exponent measurement.

Critical slowing down is nearly absent in short-time dynamics.

Method distinguishes weak first-order from second-order phase transitions.

Abstract

An introductory review to short-time critical dynamics is given. From the scaling relation valid already in the early stage of the evolution of a system at or near the critical point, one derives power law behaviour for various quantities. By a numerical simulation of the system one can measure the critical exponents and, by searching for the best power law behaviour, one can determine the critical point. Critical slowing down as well as finite size corrections are nearly absent, since the correlation length is still small for times far before equilibrium is reached. By measuring the (pseudo) critical points it is also possible to distinguish (weak) first-order from second-order phase transitions.