The structure of Gibbs states and phase coexistence for non-symmetric continuum Widom Rowlinson models

Abstract

We prove the existence of phase transitions in non-symmetric r-component continuum Widom-Rowlinson models. Our results are based on an extension of the Pirogov-Sinai theory of phase transitions in general lattice spin systems to continuum systems. This generalizes Ruelle's extension of the Peierls argument for lattices to symmetric continuum Widom-Rowlinson models. The Pirogov-Sinai picture of the low temperature phase diagram for spin systems goes over into a phase-diagram of the Widom-Rowlinson model at large fugacities z=(z0,..., z r−1). There is in z-space a point where the system has r-pure phases, lines with r−1 phases, two dimensional surfaces with r−2 phases, etc.