Abstract
Present the algebraic formulation and main thermodynamic properties of spin and fermionic quantum lattice systems. Apply these notions to some concrete models as Hubbard and Falicov-Kimball ones. In particular, make use of the Pirogov-Sinai theory to study the phase diagrams at low temperatures given by perturbations in the hamiltonian, as done in two papers by Borgs and Kotecky. (AU)