Virial expansion and liquid–vapor critical points of high dimension classical fluids

Abstract

In this paper, we study the liquid–vapor transition of a classical fluid with hard sphere repulsion and short range attraction at criticality in the high dimension limit. We are motivated by physical arguments that relate the presence of percolating clusters to the critical point of the liquid–vapor transition. The volume fraction at the percolation threshold is also expected to decrease for increasing dimension. Together, these imply that the critical density may decrease with dimensionality and for sufficiently high dimension, the truncated low order virial expansion should suffice in describing the critical point. We evaluate analytically the exact second and third virial coefficients for high dimension and explicitly show the modifications of the hard sphere coefficients by the attractive part of the potentials. Then, the truncated virial expansion at criticality is used to demonstrate that the critical volume fraction indeed decreases with dimensionality. This will allow us to propose that the truncated virial expansion provides an accurate description of fluid criticality in the high dimension limit.