Generic two-phase coexistence in nonequilibrium systems

Abstract

Gibbs' phase rule states that two-phase coexistence of a single-component system, characterized by an n-dimensional parameter-space, may occur in an n-1-dimensional region. For example, the two equilibrium phases of the Ising model coexist on a line in the temperature-magnetic-field phase diagram. Nonequilibrium systems may violate this rule and several models, where phase coexistence occurs over a finite (n-dimensional) region of the parameter space, have been reported. The first example of this behaviour was found in Toom's model [Toom,Geoff,GG], that exhibits generic bistability, i.e. two-phase coexistence over a finite region of its two-dimensional parameter space (see Section 1). In addition to its interest as a genuine nonequilibrium property, generic multistability, defined as a generalization of bistability, is both of practical and theoretical relevance. In particular, it has been used recently to argue that some complex structures appearing in nature could be truly stable rather than metastable (with important applications in theoretical biology), and as the theoretical basis for an error-correction method in computer science (see [GG,Gacs] for an illuminating and pedagogical discussion of these ideas).