Discrete Hubbard-Stratonovich transformation for fermion lattice models

We discuss a new functional-integral formulation of interacting fermion systems on a lattice such as the Anderson or Hubbard models: the fermion-fermion interaction is eliminated by introducing auxiliary Ising variables. The resulting model for a $d$-dimensional quantum system is a ($d+1\mathrm{}$)-dimensional Ising model with complicated interactions. The new transformation is particularly useful for performing numerical studies of these models using Monte Carlo techniques. We study its convergence properties and compare it with the usual Gaussian formulation for the case of the Hubbard model.