The universal repulsive-core singularity and Yang–Lee edge criticality

Abstract

In 1984 Poland proposed that lattice and continuum hard-core fluids are characterized by a singularity on the negative fugacity axis with an exponent, here called φ(d), that is universal, depending only on the dimensionality d. We show that this singularity can be identified with the Yang–Lee edge singularity in d dimensions, which occurs on a locus of complex chemical potential above a gas-liquid or binary fluid critical point (or in pure imaginary magnetic fields above a ferromagnetic Curie point) and, hence, with directed lattice animals in d+1 dimensions and isotropic lattice animals or branched polymers in d+2 dimensions. It follows that φ=3/2 for d≥6 while power series in ε=6−d can be derived for φ(d) and for the associated correction-to-scaling exponent θ(d) with θ(1)=1 and θ(2)=5/6. By examining the two-component primitive penetrable sphere model for d=1 and d=∞ and long series for the binary Gaussian-molecule mixture (GMM) for all d, we conclude that the universality of φ(d) and θ(d) extends to continuum fluid mixtures with hard and soft repulsive cores [the GMM having Mayer f functions of the form −exp(−r2/r20)]. The new estimates φ(3)=1.0877(25) and θ(3)=0.622(12) are obtained with similar results for d=4 and 5.