CORRELATION INEQUALITIES AND UNIQUENESS OF EQUILIBRIUM STATE FOR PLANE ROTATOR FERROMAGNETIC MODEL

We derive new inequalities for the plane rotator ferromagnetic model and use them to obtain the following results: 1) If the model is isotropic, the derivability of the free energy as function of the magnetic field h implies the existence of a unique translation invariant Gibbs state and if furthermore h=0 all Gibbs states are invariant by rotation of the spins. 2) If the model is anisotropic the above assertion holds for h non-zero. 3) If the model is anisotropic then there are at most two extremal translation invariant Gibbs states for almost all values of the anisotropy parameter. © 1978 Springer-Verlag.