Time-Dependent Ising-Model Description of Binary Liquid Mixtures

Abstract

Phase transitions are not only characterized by singularities in thermodynamic derivatives, but also by peculiarities in the time-dependent behavior of the system. By employing a time-dependent generalization of the Ising model and a master equation, the relaxation of a local deviation from equilibrium for a system near its critical temperature is described. Approximate solution of the equations yield results in agreement with recent optical experiments, in which the decay of concentration fluctuations in critical mixtures of liquids is measured; results are also consistent with NMR measurements in antiferromagnets. If the equations are solved more accurately, however, it is found that the decay of a local displacement from equilibrium concentration in the critical region is in general not describable by a single exponential.