Theoretical models will be presented in which the internal energy of (a) a ferromagnet and (b) a pyroelectric material is expressed in terms of magnetization and electric polarization, respectively. For the ferromagnet, simple models of elementary excitations (e.g., spin wave theory in an insulator, to which Stoner excitations must be added in a metal) lead to formulas for the internal energy at low temperature as power laws in the change of magnetization from its saturation value. An unconventional use of two order parameters, the sublattice magnetization plus the metallic discontinuity in momentum distribution at the Fermi surface, allows the phase transition between metallic and insulating states of antiferrornagnets to be treated at T = 0, the three-dimensional transition-metal dichalcogenides being an example here. The treatment of the internal energy of the ferromagnet is then extended to include the entropy also, using specifically the king model in nonzero external magnetic field. Its relevance to the Landau theory of phase transitions will be emphasized. Some comments will finally be made about the analogue for pyroelectrics. 0 1996 John Wiley & Sons, Inc.
with magnets-both ferro and antiferro-where the magnetization is the crucial quantity, and with pyroelectrics, where the polarization, or dipole moment per unit volume, plays a central role. A little more specifically, the order parameter of the transition from a paramagnetic to a ferromagnetic state with long-range magnetic order is the magnetization M . This transition is second-order; e.g., the susceptibility and specific heat, second-order