Phase Transition for a System of Two Species in Competition

#### C. Bisceglia

2009, v.15, №2, 149-190

ABSTRACT

In this article we construct a statistical mechanics model of a system studied at the "mesoscopic level" by Carlen et al. in [M.C. Carvalho, E. Carlen, R. Esposito, J.L. Lebowitz and R. Marra, Free energy minimizers for a two-species with segregation and condensation-evaporation transition, Nonlinearity, 2003, v.16, 1075-1105]. The system is a lattice gas on $Z^d$ with two species of particles (at each site there is at most one particle per species). The interaction is attractive among particles of the same species and repulsive for different species. The interaction is described by a Kac potential whose scaling parameter is denoted by $\gamma$. We prove that there is a curve of values of temperature and $\theta$, $\theta$ an external magnetic field, where three distinct DLR measures coexist. The proof is obtained by a perturbation around mean-field using the Pirogov - Sinai theory.

Keywords: Kac potentials,Lebowitz - Penrose limit,Pirogov - Sinai theory

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