Breakdown of the Onsager reaction field theory in two dimensions
  It is shown that for the spin 1/2 anisotropic Heisenberg model the result for the transition temperature is completely insensitive to the anisotropy within the Onsager reaction field theory, which yields a vanishing T_c in two dimensions, in total conflict with the expected finite T_c, increasing with anisotropy. This establishes that the breakdown of the Onsager reaction field theory in two dimensions is not limited to the Ising model, but actually extends over the whole range of anisotropy. Therefore, for the isotropic case, the results of vanishing T_c and exponential dependence of spin correlation length should be seen as mere coincidence. 
Avinash Singh