Abstract
The Kirkwood expansion for spin systems involving a priori averages within states of a given long-range order in the cumulant expansion of the free energy is examined. By defining a generating function for the averages the inconvenient averages can be replaced by a suitable canonical average in the thermodynamic limit. This modified Kirkwood expansion is generalized to the case of arbitrary spin. Simple applications to the Ising model and the spin one model of 3He-4He mixtures are illustrated. A two-spin cluster approximation for the Ising model gives estimates of the critical temperature in good agreement with the Bethe-Peierls approximation.
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