R. Ganguly, CRITICAL-POINT IN A 2-DIMENSIONAL PLANAR MODEL, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 55(5), 1997, pp. 4982-4989
Transfer matrix formalism has been used to study the phase transition
in a two-dimensional isotropic planar model where one dimension is tak
en to be spatial and the second dimension is temporal. Character expan
sion 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 be
en found in both theoretical calculation and computer simulation separ
ately for different values of temperature. From the results I infer an
algebraic divergence of correlation length rather than a Kosterlitz-T
houless type. The value of critical temperature is found to be k(B)T(c
)/J = 0.899.