Nonclassical critical behavior of the square-well fluid

In this paper we report the results of extensive numerical calculations on the equation of state of the square-well fluid in the immediate vicinity of its critical point, with the objective being the precise determination of the critical exponents $\beta$ and $\delta$. These determinations were carried out using data generated by solving the Yvon-Born-Green equation for the pair distribution function (with superposition approximation) over an extended range of integration (∼50 intermolecular diameters). When taken together with the value of the critical exponent $\gamma$ reported previously by the authors ($\gamma =1.24\mathrm{}\pm 0.04$), the results obtained, $\beta =0.330\mathrm{}\pm 0.008$ and $\delta =4.4\mathrm{}\pm 0.2$, suggest strongly that the essential physics of the gas-liquid transition in the neighborhood of the critical point is described correctly by an integral equation derived from the classical Bogoliubov-Born-Green-Kirkwood-Yvon theory of distribution functions.