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Purification and uniqueness of quantum Gibbs states

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Abstract

We give a new condition for uniqueness of Gibbs states of quantum spin models on lattices.

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References

  1. Araki, H., Ion, P.: On equivalence of KMS and Gibbs conditions for states of quantum lattice systems. Commun. Math. Phys.35, 1–12 (1974)

    Article  Google Scholar 

  2. Bratteli, O., Robinson, D.: Operator Algebras and Quantum Statistical Mechanics. Vol. I and II, Berlin, Heidelberg, New York: Springer

  3. Bratteli, O., Robinson, D.: Unbounded derivation of von Neumann algebras. Ann. Inst. Henri Poincaré25, 159–164 (1976)

    Google Scholar 

  4. Dobrushin, R.L.: Theory Probab. Its Appl.13, 13, 197–224 (1968)

    Google Scholar 

  5. Dobrushin, R.L.: Shlosman, B.: Constructive criterion for the uniqueness of Gibbs field. In: Statistical Physics and Dynamical Systems. Rigorous Results, Basel, Birkhäuser: 1985, pp. 347–370

    Google Scholar 

  6. Kossakowski, A., Frigerio, A., Gorini, V., Verni, M.: Detailed balance and KMS conditions. Commun. Math. Phys.57, 97–110 (1977)

    Article  Google Scholar 

  7. Matsui, T.: Markov semigroups on UHF algebras. To appear

  8. Stroock, D.W., Zegalinski, B.: The logarithmic Sobolev inequality for discrete spin systems on a lattice. Commun. Math. Phys.149, 175–193 (1992)

    Article  Google Scholar 

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Authors and Affiliations

  1. Institute for Theoretical Physics, University of Leuven, Belgium

    Taku Matsui

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  1. Taku Matsui
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Communicated by H. Araki

Research fellow of Canon Foundation in Europe, on leave from Tokyo Metropolitan University, Hachioji, 192-03 Japan

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Matsui, T. Purification and uniqueness of quantum Gibbs states. Commun.Math. Phys. 162, 321–332 (1994). https://doi.org/10.1007/BF02102020

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  • DOI: https://doi.org/10.1007/BF02102020

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