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New Condition on Uniqueness of Gibbs Measure for Models with Uncountable Set of Spin Values on a Cayley Tree

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Abstract

In this paper we consider a model with nearest-neighbor interactions with spin space [0, 1] on Cayley trees of order k ⩾ 2. In Yu et al. (2013), a sufficient condition of uniqueness for the splitting Gibbs measure of the model is given. We investigate the sufficient condition of uniqueness and obtain better estimates.

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Acknowledgements

I should like to thank the referees for careful reading of the manuscript; in particular, for a number of suggestions which have improved the paper.

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  1. National University of Uzbekistan, University str 4 Olmazor district, Tashkent, 100174, Uzbekistan

    F. H. Haydarov

  2. AKFA University, 17, Kichik Halqa Yuli Street, Tashkent City, 100095, Uzbekistan

    F. H. Haydarov

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  1. F. H. Haydarov
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Correspondence to F. H. Haydarov.

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Haydarov, F.H. New Condition on Uniqueness of Gibbs Measure for Models with Uncountable Set of Spin Values on a Cayley Tree. Math Phys Anal Geom 24, 31 (2021). https://doi.org/10.1007/s11040-021-09404-3

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  • DOI: https://doi.org/10.1007/s11040-021-09404-3

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