Abstract
We introduce a method for computing corrections to the Bethe approximation for spinmodels on arbitrary lattices. Unlike cluster variational methods, the new approach takesinto account fluctuations on all length scales.The derivation of the leading correction is explained and appliedto two simple examples: the ferromagnetic Ising model ond-dimensional lattices, and the spin glass on random graphs (both in their high-temperaturephases). In the first case we rederive the well known Ginzburg criterion and the uppercritical dimension. In the second, we compute finite-size corrections to the free energy.
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