Universal relations among thermodynamic critical amplitudes

Abstract

The hypothesis of universality implies that there are four universal ratios among the six usually defined thermodynamic critical amplitudes. Theoretical information from series and $\epsilon$ expansions is presented on the values of these ratios for short-ranged Ising, Heisenberg, and spherical models, and for dipolar systems. A number of real materials are discussed (Xe, ${\mathrm{CO}}_2$, Ni, EuO, and ${\mathrm{LiTbF}}_4$), and the present state of our understanding of the thermodynamic ratios for these systems is found to be rather crude.