Thermodynamic Stability and Critical Point in Simple Fluids and Ferromagnets

Abstract

By using a rigorous characterization of a critical point, based on Tisza's thermodynamic theory of phase transitions, we have obtained for simple fluids and ferromagnets, in a unified way and without making additional hypotheses, the usual and new inequalities among critical indices. In contrast to the previous thermodynamic attempts, we have been able to establish when the index relations are valid as strict equalities. Furthermore, we have derived expressions for some critical indices in terms of critical amplitudes; then the possibility of finite cusps and discontinuities for the specific heats at the critical point has been explicitly considered and the precise connection between the static scaling hypotheses and the thermodynamic stability has been established. Finally we have stressed the analogy between fluids and ferromagnets and pointed out some important differences which follow from the slope of the saturation curve being zero for ferromagnets, unlike that for fluids. For ferromagnets it is also proved that, when the Rushbrooke (Griffiths) index relation is valid as a strict equality, it results in 0<β<1, where β is the phase-boundary critical index. Incidentally, the paper gives several results which are in agreement with the experimental evidence obtained within the stability framework.