LOCAL PERTURBATIONS AND LIMITING GIBBS-STATES OF QUANTUM-LATTICE MEAN-FIELD SYSTEMS

In the frame of operator algebraic quantum statistical mechanics, the limiting Gibbs states for quantum lattice mean-field systems under the influence of weak perturbations are analyzed. For a certain model cla ss it is proved that all homogeneous states which minimize the functio nal of the free energy density, can be calculated as the thermodynamic limit of perturbed local Gibbs states. For uniformly bounded nets of (not necessarily homogeneous) local perturbations with a well defined asymptotical behaviour in the thermodynamic limit (approximately symme tric, resp. quasi-symmetric nets) the existence of a unique limiting G ibbs state is proved for the considered model class. An inhomogeneous BCS-model and the Josephson junction of coupled superconductors are ex amples for the applicability of the results. Finally, the relation of the considered local perturbations to extended-valued lower-bounded op erators affiliated with a von Neumann algebra as relative Hamiltonians of two normal states is discussed.