EXACT SOLUTIONS FOR INFINITE-RANGE SPIN HAMILTONIANS

The closed form magnetization equation, s=σ·B σ[-β·σ∂H/∂s], is shown to be valid for any infinite range spin Hamiltonian H=N·H(s), where N is the number of particles, each with elementary spin σ, s=S/N, S being the total spin, and Bσ is Brillouin's function. This equation is used to investigate the following problems: (i) determination of the class of Hamiltonians with a spinodal point at 0°K; (ii) spin-phonon coupling, quadratic in the lattice displacements. Magnetostriction of this form may lead to shift of the critical temperature, change of the order of the phase transition, decrease of the paramagnetic spinodal temperature up to 0°K and renormalization of the phonon spectrum; (iii) singlet-ground-state ferromagnetism, exhibiting various types of phase-transitions, including heat magnetization.