“Almost” mean-field Ising model: An algebraic approach. (English) Zbl 0945.82503
Summary: We study the thermodynamic limit of the algebraic dynamics for an “almost” mean-field Ising model, which is a slight generalization of the Ising model in the mean-field approximation. We prove that there exists a family of “relevant” states on which the algebraic dynamics \(\alpha^t\) can be defined. This \(\alpha^t\) defines a group of automorphisms of the algebra obtained by completing the standard spin algebra with respect to the quasiuniform topology defined by our states.
MSC:
| 82B10 | Quantum equilibrium statistical mechanics (general) |
| 82C10 | Quantum dynamics and nonequilibrium statistical mechanics (general) |
| 81T27 | Continuum limits in quantum field theory |
| 46L60 | Applications of selfadjoint operator algebras to physics |
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