Analyticity properties of the anisotropic Heisenberg model}

An upper bound Te for the critical temperature of a class of spin systems which includes the Heisenberg ferromagnet is derived. The analyticity of the free energy as a function of the temperature, the external magnetic field, and the interaction potentials, is demonstrated in a domain which includes all tem- peratures T > Tc For the isotropic Heisenberg ferromagnet in v dimensions we find the poor estimate 2vJ/JcT0 = 0.0001. Some analyticity and cluster properties of the reduced density matrices are also derived