Cluster expansion

Summary

A cluster expansion writes the logarithm of a partition function as a power series. Its terms are sums over connected clusters of particles or of other objects. In the classical form, due to Mayer, the pressure of a gas is expanded in powers of the activity. Its coefficients are integrals of products of Mayer f-functions over connected graphs. When the series converges it proves that the system is in a single phase with analytic thermodynamic functions and fast decay of correlations. Abstract versions for polymer systems are a main tool of rigorous statistical mechanics.