Equation of state near the endpoint of the critical line

We discuss first-order transitions for systems in the Ising universality class. The critical long distance physics near the endpoint of the critical line is explicitly connected to microscopic properties of a given system. Information about the short distance physics can therefore be extracted from the precise location of the endpoint and non-universal amplitudes. Our method is based on non-peturbative now equations and yields directly the universal features of the equation of state, without additional theoretical assumptions of scaling or resummations of perturbative series. The universal results compare well with other methods. We present new universal properties for the dependence of the correlation length on large fields. We also compute non-universal critical amplitudes for carbon dioxide. (C) 1999 Elsevier Science B.V. All rights reserved.