Mean-Field Theory of the Potts Gas
Résumé
We consider a gas of classical particles in $\mathbb{R}^d$ having $q$ distinct colours, interacting via a mean-field Potts potential, and subject to an external field; a colour-independent molecular interaction of mean-field type is also admitted. In contrast to the usual lattice Potts model, the Potts gas exhibits the specific volume $v$ as a parameter, in addition to colour-ordering. The $v$-dependence of the Potts gas is studied in detail, and the complete phase diagram is derived. It turns out that, for $q\ge3$, the transition to colour-ordering implies a jump of density. For $q=2$, this transition is continuous but may become discontinuous under the influence of a suitable molecular interaction.
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