On the Decay of Correlations in Non-Analytic SO(n)-Symmetric Models

: We extend the method of complex translations which was originally employed by McBryan-Spencer [2] to obtain a decay rate for the two point function in two-dimensional SO(n)-symmetric models with non-analytic Hamiltonians for n 2. 1. Introduction The Mermin-Wagner theorem [3] rules out the possibility of having a spontaneous symmetry breaking at non-zero temperatures for the two dimensional Heisenberg model. As a result, the two point function for this model at non-zero temperature decays to zero at large spatial separations. This theorem, however, does not give any rate for the decay of the two point function. McBryan and Spencer [1, 2] employed the method of complex translation to get the expected power law decay (for low temperatures). Although the analyticity of the interaction seems to be crucial in their argument, this is the purpose of the present paper to show that a proper modification of their method gives similar bounds with much weaker assumptions, namely we will obtain ..