  We start from a low-energy effective field theory for interacting fermions on
the lattice and expand in the hopping parameter to derive the nearest-neighbor
interactions for a lattice gas model. In this model the renormalization of
couplings for different lattice spacings is inherited from the effective field
theory, systematic errors can be estimated a priori, and the breakdown of the
lattice gas model description at low temperatures can be understood
quantitatively. We apply the lattice gas method to neutron matter and compare
with results from a recent quantum simulation.
