Abstract
We observe that for finite N and V, the canonical partition function Q(N) of a fluid system of N particles is a polynomial of degree N in variable V/Nlambda(3), which has N zeros that depend only on the cluster integrals b(2)(V,T), em leader,b(N)(V,T). In the thermodynamic limit, if the zero distribution approaches the positive real axis, a phase transition arises. The behavior of phase transition is determined solely by the zero distribution near the positive real axis. Below the critical temperature, the Maxwell's equal-area rule must be used to obtain the gas-liquid coexistence regime. Several examples are given.
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