Abstract

Two lower bounds for the free energy of the Hubbard model are compared. One of the basic tasks in quantum statistics is the calculation the grand thermodynamic potential Q or Helmholtz free energy F for a given Hamiltonian-operator H. In almost all cases the free energies can-not be exactly calculated. Thus it is helpful to find upper and lower bounds for the free energies. Upper bounds are mainly based on the inequality [1, 2] . Ä Ä