Effective dynamics of the quantum mechanical Weiβ-Ising model

The quantum-mechanical Weiβ-Ising model is discussed anew in the light of recent results of algebraic quantum mechanics. The limiting Gibbs states are calculated by direct convergence estimations. Starting from the molecular field operator the dynamics is constructed in every temperature representation. The spectra of the effective Hamiltonians are determined by means of the Connes theory. The representations of the quasilocal algebra given by the pure phase states below the transition temperature are shown to be factors of type IIIλ, λ ∈ (0, 1). An infinity of ground states together with their effective Hamiltonians are constructed and investigated.