95-526 Georgii H.-O., H\"aggstr\"om O.

Phase transition in continuum Potts models (66K, LaTex) Dec 13, 95

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Abstract. We establish phase transitions for a class of continuum multi--type particle systems with finite range repulsive pair interaction between particles of different type. This proves an old conjecture of Lebowitz and Lieb. A phase transition still occurs when we allow a background pair interaction (between all particles) which is superstable and has sufficiently short range of repulsion. Our approach involves a random--cluster representation analogous to the Fortuin--Kasteleyn representation of the Potts model. In the course of our argument, we establish the existence of a percolation transition for Gibbsian particle systems with random edges between the particles, and also give an alternative proof for the existence of Gibbs measures with superstable interaction.

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