- 95-526 Georgii H.-O., H\"aggstr\"om O.
- Phase transition in continuum Potts models
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.