Abstract:
We study p-adic hard core models with three states on the Cayley tree. It is known that there are four types of such models. We find conditions that must be imposed on the order k of the Cayley tree and on the prime p for a translation-invariant p-adic Gibbs measure to exist.
Citation:
O. N. Khakimov, “p-Adic Gibbs measures for the hard core model with three states on the Cayley tree”, TMF, 177:1 (2013), 68–82; Theoret. and Math. Phys., 177:1 (2013), 1339–1351
\Bibitem{Kha13}
\by O.~N.~Khakimov
\paper $p$-Adic Gibbs measures for the~hard core model with three states on the~Cayley tree
\jour TMF
\yr 2013
\vol 177
\issue 1
\pages 68--82
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\transl
\jour Theoret. and Math. Phys.
\yr 2013
\vol 177
\issue 1
\pages 1339--1351
\crossref{https://doi.org/10.1007/s11232-013-0107-0}
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Linking options:
https://www.mathnet.ru/eng/tmf8603
https://doi.org/10.4213/tmf8603
https://www.mathnet.ru/eng/tmf/v177/i1/p68
This publication is cited in the following 7 articles:
J G Polli, E P Raposo, G M Viswanathan, M G E da Luz, “Stochastic-like characteristics of arithmetic dynamical systems: the Collatz hailstone sequences”, J. Phys. Complex., 5:1 (2024), 015011
Tukhtabaev A., “On G(2)-Periodic Quasi Gibbs Measures of P-Adic Potts Model on a Cayley Tree”, P-Adic Numbers Ultrametric Anal. Appl., 13:4 (2021), 291–307
Khakimov O. Mukhamedov F., “Chaotic Behavior of the P-Adic Potts-Bethe Mapping II”, Ergod. Theory Dyn. Syst., 2021, PII S0143385721000961
M. M. Rahmatullaev, O. N. Khakimov, A. M. Tukhtaboev, “A p-adic generalized Gibbs measure for the Ising model on a Cayley tree”, Theoret. and Math. Phys., 201:1 (2019), 1521–1530
Rahmatullaev M. Tukhtabaev A., “Non Periodic P-Adic Generalized Gibbs Measure For Ising Model”, P-Adic Numbers Ultrametric Anal. Appl., 11:4 (2019), 319–327
O. N. Khakimov, “p-Adic solid-on-solid model on a Cayley tree”, Theoret. and Math. Phys., 193:3 (2017), 1880–1893
O. N. Khakimov, “A p-adic hard-core model with three states on a Cayley tree”, Siberian Math. J., 57:4 (2016), 726–734
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