Interactions and pressure functionals for disordered lattice systems (Q1180979)

An attempt is made to provide a theoretical framework for disordered spin systems on a lattice similar to the one of a classical statistical mechanics in the sense of Ruelle. The proof is given of the existence of nonrandom continuous pressure functionals defined on Banach space of ``random bond'' type interaction. The similar result is obtained for the replica systems. An analog of the classical variational principle is formulated which provides an a priori meaning of infinite equilibrium state of a disordered system. The possible reasonable extensions of long range ``random site'' type interaction are discussed and for some class of them the existence and continuity of the infinite volume pressure for spin system is proven.