High dimensionality as an organizing device for classical fluids

The Mayer diagrammatic expansion for a classical pair-interacting fluid in thermal equilibrium is cast in a form particularly appropriate to high-dimensional space. At asymptotically high dimensionality, the series, when it converges, is dominated by a single term. Focusing upon repulsive interactions, the dominant term belongs to a ring diagram and can have either sign, but when negative, the series must diverge. The nature of the divergence is found explicitly for hard core interactions, and analytic extension in density obtained by summing up the dominant ring contributions. The result is that a second virial truncation remains valid at densities much higher than that at which the series diverges. Corrections first appear in the vicinity of a particle volume-scaled density of $\frac{1}{2}{\mathrm{}(e/2\mathrm{})\mathrm{}}^{1/2}$ per dimension, and produce a spinodal in the equation of state. Suggestions are made as to elucidating the resulting phase transition.