Transport Coefficients near the Critical Point: A Master-Equation Approach

Abstract

Kawasaki has shown how to construct a nonequilibrium theory which relaxes to an equilibrium described by the standard Ising model. The main significance of Kawasaki's work is his proof that transport coefficients do not diverge near the critical point in his model. In this paper, his approach is generalized. Two master-equation models of transport are examined: one gives spin diffusion and thermal diffusion but no sound waves; the other gives thermal diffusion and sound waves. The first model involves a Hermitian transition matrix in the master equation. The Hermiticity enables one to prove a variational theorem which requires the transport coefficients to be finite. However, sound waves appear as complex eigenvalues of the relaxation time. Hence, they must come from a non-Hermitian master equation. A model is constructed which includes sound waves. In this case, the proof of the finiteness of transport coefficients fails. Aside from formal questions, the main physical point of this paper is the speculation that infinities in transport coefficients might be tied to the existence of oscillatory transport modes (like sound waves) coupled into the dynamics of the phase transition.