Planar spin system with annealed bond disorder

This is a study of the equilibrium statistical mechanics of a mixed system of planar spins and Ising spins. The Ising spins σ_r are situated (one on each of the bonds connecting the planar spins s_r so that the planar spins interact only via Ising spins. For a one-dimensional lattice the partition function and the two-spin correlation functions (σ_rσ_r¹ and S_r·S_r¹) are calculated ex actly in terms of modified Bessel functions.

For a two-dimensional anisotropic generalization of the model an equation is given for the critical temperature and the equation is shown to have one and only one solution T_c such that 0<T_c<∞.