Theory of one- and two-dimensional magnets with an easy magnetization plane. II. The planar, classical, two-dimensional magnet

A new approach to the 2-D classical planar magnet is proposed. The Hamiltonian is replaced by an approximate one, which, in contrast with previous approximations, preserves the correct symmetry of the problem; the existence of a phase transition without long range order at some temperature Tc is confirmed; quantitative evaluations of the spin pair correlation function below T c, and of the transition temperature Tc are given; the results are in good agreement at low T with the self consistent harmonic approximation (S.C.H.A.). A transition is predicted at a temperature KB Tc = 1.7 Js2, in very good agreement with predictions based on series expansions, whereas the critical exponents are those predicted by Kosterlitz, in particular γ = ∞.