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Ground States and Gibbs Measures for the Potts-SOS Model with an External Field on the Cayley Tree

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Abstract

We consider the Potts-SOS model with non-zero external field on the Cayley tree. We describe the ground states for the Potts-SOS model with a translation-invariant external field. We verify the Peierls condition for the model. Using a contour argument, we show the existence of two different Gibbs measures at sufficiently low temperatures. Periodic ground states for the Potts-SOS model with a periodic external field are also found.

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This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.

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Authors and Affiliations

  1. Institute of Mathematics, 100174, Tashkent, Uzbekistan

    M. M. Rahmatullaev & M. A. Rasulova

  2. New Uzbekistan University, 100000, Tashkent, Uzbekistan

    M. M. Rahmatullaev

  3. Namangan State University, 160136, Namangan, Uzbekistan

    M. M. Rahmatullaev & M. A. Rasulova

Authors
  1. M. M. Rahmatullaev
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  2. M. A. Rasulova
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Correspondence to M. M. Rahmatullaev or M. A. Rasulova.

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Rahmatullaev, M.M., Rasulova, M.A. Ground States and Gibbs Measures for the Potts-SOS Model with an External Field on the Cayley Tree. Lobachevskii J Math 45, 518–531 (2024). https://doi.org/10.1134/S1995080224010451

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