Onsager reaction field theory for the three-dimensional anisotropic XY model

We discuss coupled XY spin chains in three dimensions and calculate the transition temperature and spin correlation lengths as functions of the ratio of the interchain exchange coupling J^′ to the intrachain coupling J, for chainlike spatial anisotropy J^′<J. We use two different approaches of the Onsager reaction-field (ORF) formalism. First we use the standard ORF theory, in which both the intrachain and interchain couplings are treated equally. Second, we treat one chain exactly and consider it in the effective field caused by the other chains, with the ORF formalism applied to the interchain interaction. The transition temperatures obtained are compared with results from Monte Carlo simulations.