Statistical Mechanics of Dense Matter: A New Self-Consistent Field Theory

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Abstract
A new ``self‐consistent field'' method in classical statistical mechanics is described. For lattice systems with nearest‐neighbor interactions the method is equivalent to the Bethe or quasichemical approximation. However it is more readily generalized to apply to more complicated systems with further‐neighbor interactions, provides insight into the physical meaning of the approximation, and provides the basis for a perturbation theory leading to expansions which are at least formally convergent. Application to lattice models of dense matter leads to integral equations which can presumably be solved by iteration. For a one‐dimensional system of hard lines the integral equation derived using the new method and a cell model can be solved exactly and the result is identical at all densities with the known exact expression for the partition function, as it should be since the perturbation corrections all vanish in this case.

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