Phase transitions for a continuous system of classical particles in a box
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A continuous classical system involving an infinite number of distinguishable particles is analyzed along the same lines as its quantum analogue, considered in [1]. A commutative C*-algebra is set up on the phase space of the system, and a representation-dependent definition of equilibrium involving the static KMS condition is given. For a special class of interactions the set of equilibrium states is realized as a convex Borel set whose extremal states are characterized by solutions to a system of integral equations. By analyzing these integral equations, we prove the absence of phase transitions for high temperature and construct a phase transition for low temperature. The construction also provides an example of a translation-invariant state whose decomposition at infinity yields states that are not translation-invariant. Thus we have an example in the classical situation of continuous symmetry breaking. 1977 Springer-Verlag.