THE UNIVERSAL REPULSIVE-CORE SINGULARITY AND YANG-LEE EDGE CRITICALITY

In 1984 Poland proposed that lattice and continuum hard-core fluids ar e characterized by a singularity on the negative fugacity axis with an exponent, here called phi(d), that is universal, depending only on th e dimensionality d. We show that this singularity can be identified wi th the Yang-Lee edge singularity in d dimensions, which occurs on a lo cus of complex chemical potential above a gas-liquid or binary fluid c ritical point (or in pure imaginary magnetic fields above a ferromagne tic Curie point) and, hence, with directed lattice animals in d+1 dime nsions and isotropic lattice animals or branched polymers in d+2 dimen sions. It follows that phi=3/2 for d greater than or equal to 6 while power series in epsilon=6-d can be derived for phi(d) and for the asso ciated correction-to-scaling exponent theta(d) with theta(1)=1 and the ta(2)=5/6. By examining the two-component primitive penetrable sphere model for d=1 and d=infinity and long series for the binary Gaussian-m olecule mixture (GMM) for all d, we conclude that the universality of phi(d) and theta(d) extends to continuum fluid mixtures with hard and soft repulsive cores [the GMM having Mayer f functions of the form -ex p(-r(2)/r(0)(2))]. The new estimates phi(3)=1.0877(25) and theta(3)=0. 622(12) are obtained with similar results for d=4 and 5. (C) 1995 Amer ican Institute of Physics.