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Construction of an uncountable number of limiting Gibbs measures in the inhomogeneous ising model

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Abstract

We prove the existence of an uncountable number of limiting Gibbs measures in the inhomogeneous Ising model on a Cayley tree and describe them constructively.

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References

  1. U. A. Rozikov,Theor. Math. Phys.,112, 929–933 (1997).

    MATH  MathSciNet  Google Scholar 

  2. N. N. Ganikhodzhaev,Dokl. Akad. Nauk Resp. Uzbekistan, No. 5, 3–6 (1994).

    Google Scholar 

  3. N. N. Ganikhodzhaev and U. A. Rozikov,Theor. Math. Phys.,111 480–486 (1997).

    MATH  MathSciNet  Google Scholar 

  4. P. M. Bleher,Commun. Math. Phys.,128, 411–419 (1990).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  5. S. Katsura and M. Takizawa,Progr. Theor. Phys.,51, 82–98 (1974).

    Article  ADS  Google Scholar 

  6. R. L. Dobrushin,Teor. Veroyatn. Primenen.,18, 261–279 (1973).

    Google Scholar 

  7. P. M. Blekher and N. N. Ganikhodzhaev,Theory Probab. Appl.,35, 216–227 (1990).

    Article  MATH  MathSciNet  Google Scholar 

  8. N. N. Ganikhodzhaev and U. A. Rozikov,Uzbek. Mat. Zh., No.4, 8–19 (1995).

    MathSciNet  Google Scholar 

  9. N. N. Ganikhodzhaev,Theor. Math. Phys.,85, 1125–1133 (1990).

    Article  MathSciNet  Google Scholar 

  10. C. J. Preston,Gibbs States on Countable Sets, Cambridge Univ. Press, Cambridge (1974).

    MATH  Google Scholar 

  11. F. Spitzer,Ann. Prob.,3, 387–398 (1975).

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Romanovskii Institute for Mathematics, Republic of Uzbekistan Academy of Sciences, Tashkent, Republic of Uzbekistan

    U. A. Rozikov

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  1. U. A. Rozikov
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 118, No. 1, pp. 95–104, January, 1999.

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Rozikov, U.A. Construction of an uncountable number of limiting Gibbs measures in the inhomogeneous ising model. Theor Math Phys 118, 77–84 (1999). https://doi.org/10.1007/BF02557197

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  • DOI: https://doi.org/10.1007/BF02557197

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