
Statistics 2005
How to Compute Loop Corrections to Bethe ApproximationDOI: 10.1088/17425468/2005/10/P10011 Abstract: We introduce a method for computing corrections to Bethe approximation for spin models on arbitrary lattices. Unlike cluster variational methods, the new approach takes into account fluctuations on all length scales. The derivation of the leading correction is explained and applied to two simple examples: the ferromagnetic Ising model on ddimensional lattices, and the spin glass on random graphs (both in their hightemperature phases). In the first case we rederive the wellknown Ginzburg criterion and the upper critical dimension. In the second, we compute finitesize corrections to the free energy.
