Determination of the dynamic critical exponent by quench kinetics simulations.

Abstract

A two-dimensional lattice-gas model was quenched from a disordered state to the maximum critical temperature of a 2\ifmmode\times\else\texttimes\fi{}1 superstructure and its ordering kinetics studied by Monte Carlo simulation. The critical growth exponent ${\mathit{n}}_{\mathit{c}}$ was determined from the time evolution 〈${\mathrm{\ensuremath{\Psi}}}^{2}$${\mathrm{〉}}_{\mathit{t}}$\ensuremath{\sim}${\mathit{t}}_{\mathit{c}}^{2\mathit{n}}$ of the scalar 2\ifmmode\times\else\texttimes\fi{}1 order parameter \ensuremath{\Psi}. The relation z=(2-\ensuremath{\eta})/2${\mathit{n}}_{\mathit{c}}$ (with static critical exponent \ensuremath{\eta}=1/4) was then applied to evaluate the (linear) dynamic critical exponent z. With Kawasaki dynamics the exact value z=2 of model C of critical dynamics (nonconserved order parameter, conserved density) was recovered whereas a value z=2.19\ifmmode\pm\else\textpm\fi{}0.04 resulted for model A (nonconserved order parameter and density) with Glauber dynamics.