Order-Parameter Relaxation Times of Finite Three-Dimensional Ising-like Systems.

Abstract

We present field-theoretic and numerical studies of finite-size effects on the exponential relaxation times ${\ensuremath{\tau}}_{1}$ and ${\ensuremath{\tau}}_{2}$ of the order parameter and the square of the order parameter near the critical point of three-dimensional Ising-like systems. Finite-size scaling functions of ${\ensuremath{\tau}}_{1}$ and ${\ensuremath{\tau}}_{2}$ are calculated for the relaxational dynamics of the ${\ensuremath{\phi}}^{4}$ model in cubic geometry with periodic boundary conditions. At ${T}_{c}$ we predict the universal ratio $\frac{{\ensuremath{\tau}}_{1}}{{\ensuremath{\tau}}_{2}}=5.4$. Below ${T}_{c}$, a maximum of ${\ensuremath{\tau}}_{2}$ is predicted. New Monte Carlo data for the Ising model are presented which are in good agreement with the predictions.