Recent research shows that the partition function for a class of models
involving fermions can be written as a statistical mechanics of clusters with
positive definite weights. This new representation of the model allows one to
construct novel algorithms. We illustrate this through models consisting of
fermions with and without spin. A Hubbard type model with both attractive and
repulsive interactions becomes tractable using the new approach. Precision
results in the two dimensional attractive model confirm a superfluid phase
transition in the Kosterlitz-Thouless universality class.