Low temperature phase diagrams of fermionic lattice systems

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.