Ordering and Demixing Transitions in Multicomponent Widom-Rowlinson Models

TL;DR

This study investigates phase transitions in multicomponent Widom-Rowlinson models on a square lattice, revealing how the number of species influences the nature of gas, demixed, and crystal phases, with transitions characterized by Monte Carlo and analytical methods.

Contribution

It provides a detailed analysis of ordering and demixing transitions in multicomponent Widom-Rowlinson models, including the identification of phase types and transition orders for various numbers of species.

Findings

For 2-6 species, a direct gas to demixed transition occurs.

For 7 or more species, an intermediate crystal phase appears.

Transitions at high species number are first order, consistent with Potts model universality.

Abstract

We use Monte Carlo techniques and analytical methods to study the phase diagram of multicomponent Widom-Rowlinson models on a square lattice: there are M species all with the same fugacity z and a nearest neighbor hard core exclusion between unlike particles. Simulations show that for M between two and six there is a direct transition from the gas phase at z < z_d (M) to a demixed phase consisting mostly of one species at z > z_d (M) while for M \geq 7 there is an intermediate ``crystal phase'' for z lying between z_c(M) and z_d(M). In this phase, which is driven by entropy, particles, independent of species, preferentially occupy one of the sublattices, i.e. spatial symmetry but not particle symmetry is broken. The transition at z_d(M) appears to be first order for M \geq 5 putting it in the Potts model universality class. For large M the transition between the crystalline and demixed phase at z_d(M) can be proven to be first order with z_d(M) \sim M-2 + 1/M + ..., while z_c(M) is argued to behave as \mu_{cr}/M, with \mu_{cr} the value of the fugacity at which the one component hard square lattice gas has a transition, and to be always of the Ising type. Explicit calculations for the Bethe lattice with the coordination number q=4 give results similar to those for the square lattice except that the transition at z_d(M) becomes first order at M>2. This happens for all q, consistent with the model being in the Potts universality class.