Universal relations among thermodynamic critical amplitudes

The hypothesis of universality implies that there are four universal ratios among the six usually defined thermodynamic critical amplitudes. Theoretical information from series and ε 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, CO₂, Ni, EuO, and LiTbF₄), and the present state of our understanding of the thermodynamic ratios for these systems is found to be rather crude.