The shape of the van der Waals loop and universal critical amplitude ratios

Abstract

Assuming that a van der Waals loop for a fluid, ferromagnet, etc, can be defined, its shape is analysed on the basis of universal critical amplitude ratios for three-dimensional Ising-type systems. Selected estimates for these ratios are tabulated. Near criticality, the loop attains a universal scaled form given, optimally, by a new parametric extended sine model for the bulk asymptotic equation of state; but a (particular) low-order interpolating Padé approximant provides a reasonable fit. Among other universal features, the reduced spinodal magnetization/density and conjugate field are found to be in contrast to the van der Waals values : thus the spinodal lies appreciably closer to the binodal (or coexistence curve) than predicted classically.