THERMODYNAMIC FORMALISM AND PHASE-TRANSITIONS OF GENERALIZED MEAN-FIELD QUANTUM-LATTICE MODELS

The general structure of thermodynamic equilibrium states for a class of quantum mechanical (multi-lattice) systems is elaborated, combining quantum statistical and thermodynamical methods. The quantum statisti cal formulation is performed in terms of recent operator algebraic con cepts emphasizing the role of the permutation symmetry due to homogene ous coarse graining and employing the internal symmetries. The variati onal principle of the free energy functional is derived, which determi nes together with the symmetries the general form of the limiting Gibb s states in terms of their central decomposition. The limiting minimal free energy density and its possible equilibrium states are analyzed on various levels of the description by means of convex analysis, wher e the Fenchel transforms of the free energies provide entropy like pot entials. On the thermodynamic level a modified entropy surface is obta ined, which specifies only in combination with its concave envelope th e regions of pure and mixed phase states. The symmetry properties of a certain model allow to specify the (non-) differentiability of the mi nimal free energy density. A characterization and classification of ph ase transitions in terms of quantum statistical equilibrium states is proposed, and the connection to the Landau theory is established demon strating that the latter implies a (continuous) deformation of the set s of equilibrium states along a canonically given curve.