Critical behaviour of an isotropic spin system. I

Critical properties of a lattice model of isotropically interacting 'continuous spins' are studied using high-temperature series expansions. Both the spin-spin and spin-field interactions are different from the planar classical Heisenberg model, yet the ground-state symmetry is the same. The model is found to behave in most respects like the planar classical Heisenberg model, and in three dimensions the following values of critical indices are found: gamma =1.32+or-0.04 and alpha =-0.04+or-0.06. In two dimensions there is flimsy evidence for a divergent susceptibility with an exponent gamma approximately=3'. The results support the belief that for finite-range interaction and fixed dimensionality, unrenormalized critical indices are determined by the underlying symmetry.