We consider fermionic lattice systems with Hamiltonian H = H(0) + lambda H-
Q, where H-(0) is diagonal in the occupation number basis, while H-Q is a s
uitable "quantum perturbation". We assume that H-(0) is a finite range Hami
ltonian with finitely many ground states and a suitable Peierls condition f
or excitations, while H-Q is a finite range or exponentially decaying Hamil
tonian that can be written as a sum of even monomials in the fermionic crea
tion and annihilation operators. Mapping the d dimensional quantum system o
nto a classical contour system on a d + 1 dimensional lattice, we use stand
ard Pirogov-Sinai theory to show that the low temperature phase diagram of
the quantum system is a small perturbation of the zero temperature phase di
agram of the classical system, provided lambda is sufficiently small. Parti
cular attention is paid to the sign problems arising from the fermionic nat
ure of the quantum particles.
As a simple application of our methods, we consider the Hubbard model with
an additional nearest neighbor repulsion. For this model, we rigorously est
ablish the existence of a paramagnetic phase with commensurate staggered ch
arge order for the narrow band case at sufficiently low temperatures.