Canonical partition function technique

From the Hamiltonian the canonical partition function Q N, V, T, E, E ) can be calculated by using the standard techniques of statistical mechanics ... 

We know that a second way of calculating the macroscopic values is to use the canonical partition function. This is the method that we shall use from hereon in. To do so, we must construct a structure of the liquid, in order to be able evaluate the terms of interaction in the canonical partition function. Various techniques are used. We shall describe four such techniques Guggenheim s and Mie s models, extrapolated respectively from the gas and solid models, the Lennard-John and Devonshire cellular model and the cell/vacancy model. 

The partition function Z is given in the large-P limit, Z = limp co Zp, and expectation values of an observable are given as averages of corresponding estimators with the canonical measure in Eq. (19). The variables and R ( ) can be used as classical variables and classical Monte Carlo simulation techniques can be applied for the computation of averages. Note that if we formally put P = 1 in Eq. (19) we recover classical statistical mechanics, of course. 

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