Coexistence curve properties of Mermin's decorated lattice gas

Abstract

Mermin's decorated lattice gas, noteworthy for its singular coexistence curve diameter and previously studied in connection with the breakdown of the law of rectilinear diameters, is shown to display in addition a rich variety of coexistence curve shapes and kinds of critical behavior as the interaction parameters of the model are varied. For an attractive decoration interaction, the coexistence curve of the model resembles, and can closely approximate, the liquid-vapor coexistence curve of real fluids. For a sufficiently repulsive decoration interaction, however, the model is shown to possess (at fixed temperature) three transitions to increasingly dense phases. These coexistence curves may feature peculiar shapes, such as necks and cusps, and they can appear inverted near the critical point; these curves terminate at either a critical point or at a maxithermal point (an analog of an azeotropic point). For discrete values of the interaction parameters, the model possesses a critical double point (the coalescence of two critical points) or a cuspoidal critical point (critical azeotropy), in which cases the critical exponents become renormalized. Qualitatively these results are found to be independent of lattice structure and spatial dimensionality d ≥ 2, and representative coexistence curves are plotted for the simple cubic lattice. Possible applications of these results are mentioned.