Breakdown of the Onsager reaction field theory in two dimensions
Avinash Singh
Abstract
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 Tc in two dimensions, in total conflict with the expected finite Tc, 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 Tc and exponential dependence of spin correlation length should be seen as mere coincidence.
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