Correlation inequalities for two-dimensional vector spin systems

A set of correlation function inequalities including Griffiths, Kelly, Sherman type inequalities are proven for a lattice system of N sites where on each site there is a vector spin [s= (sx,sz), ‖s‖=1] whose distribution of values over the unit circle is given by f (s), where f (s) =f (−s). The spins interact through two-body, anisotropic, ferromagnetic interactions. Also an external field h, hx⩾0, and hz⩾0, is present. The proof uses Gaussian random variables.