Summary.
We prove uniqueness of Euclidean Gibbs states for certain quantum lattice systems with unbounded spins. We use Dobrushin’s uniqueness criterion. The necessary estimates for the Vasershtein distance between the corresponding one-point conditional distributions with boundary conditions differing only at one side, are obtained by proving a Log-Sobolev inequality on the infinite dimensional single spin (= loop) spaces. Some important classes of concrete examples to which all this applies are discussed.
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Received: 28 February 1996 / In revised form: 9 September 1996
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Albeverio, S., Kondratiev, Y., Röckner, M. et al. Uniqueness of Gibbs states for quantum lattice systems. Probab Theory Relat Fields 108, 193–218 (1997). https://doi.org/10.1007/s004400050107
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DOI: https://doi.org/10.1007/s004400050107
- Mathematics Subject Classification (1991): Primary: 60H30. Secondary: 31C25
- 82B31