  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 d-dimensional lattices, and
the spin glass on random graphs (both in their high-temperature phases). In the
first case we rederive the well-known Ginzburg criterion and the upper critical
dimension. In the second, we compute finite-size corrections to the free
energy.
