Critical behavior of two-state, steady-state Ising systems, according to the Bragg–Williams approximation

Abstract

The Bragg–Williams (mean field) approximation is applied to an infinite arbitrary lattice of two-state enzymes, with nearest-neighbor interactions, cycling at a stable steady-state arbitrarily far from equilibrium. General equations are given for the fraction of enzymes in state 2 and for the flux. A simple numerical procedure is introduced for the determination of critical constants. A considerable sampling of results, especially on critical properties, is given. Because ’’van der Waals loops’’ are often obtained, some quite complicated, hysteresis is of course possible in the conventional way. The equations are simple enough so that the interested reader can easily generate further examples of his own, if desired. Of particular interest are special cases (a) in which the phase transition occurs in two steps and (b) in which either attractive or repulsive interactions will produce a phase transition.