Criticality in multicomponent spherical models : results and cautions

TL;DR

This paper generalizes the spherical model to multicomponent fluids, revealing unique critical behavior and a 'demagnetization effect' that distorts phase coexistence, highlighting limitations of the model for fluid systems.

Contribution

It introduces a multicomponent spherical model with multiple constraints, analyzing its critical phenomena and identifying unphysical effects specific to multicomponent systems.

Findings

Criticality occurs on a locus ending a coexistence surface.

A 'demagnetization effect' suppresses divergence of susceptibilities.

The effect arises from model symmetry and multicomponent nature.

Abstract

To enable the study of criticality in multicomponent fluids, the standard spherical model is generalized to describe an $\ns$-species hard core lattice gas. On introducing $\ns$ spherical constraints, the free energy may be expressed generally in terms of an $\ns\times\ns$ 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.