HEISENBERG-FERROMAGNET WITH HIGHER-ORDER EXCHANGE

The authors investigate the properties of ferromagnetic spin systems with higher-order exchange interactions, in particular with four-spin terms of the form (Si.Sj)(Sk.Sl) and (S i.Sj)(Sj.Sk). Using the Green function equation of motion method, and simple decoupling approximations, they obtain renormalised spin-wave energies, magnetisation curves, and critical temperatures for various strengths of the four-spin interactions. For sufficiently large values of these interactions the transition becomes first order. For comparison they also give the results of spin-wave and mean-field theories.