This article is cited in 12 papers

$p$-Adic Gibbs quasimeasures for the Vannimenus model on a Cayley tree

O. N. Khakimov

Institute of Mathematics and Information Technologies, National Academy of Sciences of Uzbekistan, Tashkent, Uzbekistan

Abstract: We study $p$-adic Gibbs quasimeasures for the Vannimenus model on the order-two Cayley tree. We especially address the problem of the boundedness of translation-invariant $p$-adic Gibbs quasimeasures. We also study periodic $p$-adic Gibbs quasimeasures.

Keywords: Cayley tree, configuration, Gibbs quasimeasure, Vannimenus model, translation-invariant measure, $p$-adic number.

Received: 18.10.2013

DOI: 10.4213/tmf8536

 English version: Theoretical and Mathematical Physics, 2014, 179:1, 395–404

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