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Gibbs random fields on a lattice: Definitions, existence, uniqueness, and phase transitions (a review of proceedings of the seminar on statistical physics at the faculty of mechanics and mathematics of the Moscow state university in 1962–1994)

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Abstract

The Moscow Grand Seminar on Statistical Physics is one of the first seminars in the world devoted to rigorous methods in statistical physics. The achievements of the seminar can be appreciated in full measure from publications by the leaders of the seminar (R.L. Dobrushin, V.A. Malyshev, R.A. Minlos, Ya.G. Sinai). This paper presents a review (far from complete) of the proceedings of the seminar. The emphasis is made on the fundamental definitions and most important results.

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Authors and Affiliations

  1. Institute for Information Transmission Problems, Russian Academy of Sciences, Bol’shoi Karetnyi per. 19 stroenie 1, Moscow, 127994, Russia

    R. A. Minlos, E. A. Pecherskii & S. A. Pirogov

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  1. R. A. Minlos
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  2. E. A. Pecherskii
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  3. S. A. Pirogov
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Correspondence to R. A. Minlos.

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Original Russian Text © R.A. Minlos, E.A. Pecherskii, S.A. Pirogov, 2013, published in Informatsionnye Protsessy, 2013, Vol. 13, No. 2, pp. 141–170.

A brief version of this review was published in Eur. Phys. J. H, 2012, vol. 37, no. 4.

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Minlos, R.A., Pecherskii, E.A. & Pirogov, S.A. Gibbs random fields on a lattice: Definitions, existence, uniqueness, and phase transitions (a review of proceedings of the seminar on statistical physics at the faculty of mechanics and mathematics of the Moscow state university in 1962–1994). J. Commun. Technol. Electron. 59, 576–594 (2014). https://doi.org/10.1134/S106422691406014X

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