Critical point in a two-dimensional planar model

Abstract

Transfer matrix formalism has been used to study the phase transition in a two-dimensional isotropic planar model where one dimension is taken to be spatial and the second dimension is temporal. Character expansion has been used to calculate the eigenvalues of the transfer matrix operator. This has ensured very rapid convergence around the critical point. Fluxes have been generated at each lattice site of the spatial dimension by Monte Carlo simulation. Mass gap and free energy have been found in both theoretical calculation and computer simulation separately for different values of temperature. From the results I infer an algebraic divergence of correlation length rather than a Kosterlitz-Thouless type. The value of critical temperature is found to be ${\mathrm{k}}_{\mathrm{B}}$${\mathrm{T}}_{\mathrm{c}}$/J=0.899.