GENERALIZED SPIN SYSTEMS AND SIGMA-MODELS

A generalization of the SU(2) spin systems on a lattice and their cont inuum limit to an arbitrary compact group G is discussed. The continuu m limits are, in general, nonrelativistic sigma-model-type field theor ies targeted on a homogeneous space G/H, where H contains the maximal torus of G. In the ferromagnetic case the equations of motion derived from our continuum Lagrangian generalize the Landau-Lifshitz equations with quadratic dispersion relation for small wave vectors. In the ant iferromagnetic case the dispersion law is always linear in the long-wa velength limit. The models become relativistic only when G/H is a symm etric space. Also discussed are a generalization of the Holstein-Prima koff representation of the SU(N) algebra, the topological term, and th e existence of the instanton-type solutions in the continuum limit of the antiferromagnetic systems.