Criticality in multicomponent spherical models: Results and cautions

Abstract

To enable the study of criticality in multicomponent fluids, the standard spherical model is generalized to describe an S -species hard-core lattice gas. On introducing S spherical constraints, the free energy may be expressed generally in terms of an SxS matrix describing the species interactions. For binary systems, thermodynamic properties have simple expressions, while all the pair correlation functions are combinations of just two eigenmodes. When only hard-core and short-range overall attractive interactions are present, a choice of variables relates the behavior to that of one-component systems. Criticality occurs on a locus terminating a coexistence surface; however, except at some special points, an unexpected "demagnetization effect" suppresses the normal divergence of susceptibilities at criticality and distorts two-phase coexistence. This effect, unphysical for fluids, arises from a general lack of symmetry and from the vectorial and multicomponent character of the spherical model. Its origin can be understood via a mean-field treatment of an XY spin system below criticality.