Ferromagnets and Simple Fluids near the Critical Point: Some Thermodynamic Inequalities

It is often assumed that thermodynamic variables have a simple power-law behavior near the liquid—vapor critical point of a simple fluid; for example, that the difference in density of saturated liquid and vapor decreases as (Tc—T)β as the temperature T approaches its critical value Tc. Thermodynamic arguments are used to derive several inequalities relating exponents which describe the behavior of the isothermal compressibility, specific heat at constant volume, and various other quantities near the critical point. Many of the inequalities apply equally to the analogous problem of a ferromagnet near its Curie point. They are based on the usual ``stability'' or ``convexity'' conditions on the thermodynamic potentials together with other plausible, but less general, hypotheses.