Large Deviation Principle for One Dimensional Vector Spin Models with Kac Potentials

We consider the one dimensional planar rotator and classical Heisenberg models with a ferromagnetic Kac potential. Below the Lebowitz­Penrose critical temperature the limit mean field theory exhibits a phase transition with a continuum of equilibrium states, indexed by the magnetization vectors. We prove a large deviation principle for the associated Gibbs measures. Then we study the system in a certain limit