Correlations at the Critical Point

Abstract

An extension of the Ornstein—Zernike approach to the determination of the radial distribution function function g (r) in the critical region is given. Nonlinear terms in the equation for the local pressure as a function of local density are introduced, the significant terms being determined from the shape of the coexistence curve. For a two-dimensional lattice gas, g2(r)—1=G2(r)∼0.86r—¼ at the critical point, in reasonable agreement with the Kaufman—Onsager result: G2(r)∼0.78r—¼. In a three-dimensional lattice gas at the critical point, G3(r)∼r—1(lnr)—½ if the coexistence curve has a quadratic top; otherwise G3(r)∼r—1.