Translation-Invariant p-Adic Gibbs Measures for the Potts Model on the Cayley Tree of Order Four
- DOI
- 10.2991/978-94-6463-014-5_4How to use a DOI?
- Keywords
- p-adic field; p-adic Gibbs measure; p-adic Potts model; translation-invariant; Cayley trees
- Abstract
Different topological structure between real and p-adic fields provides a distinct condition for solution of equations or system of equations. For example, the equation
$$x^{2} + 1 = 0$$ does not have solution over real field but it has solution over p-adic field for$$ p \equiv 1\left( {\bmod 4} \right)$$ . Meanwhile, the equation$$x^{3} = p$$ has solution in real field but not in p-adic field. It is convenience to investigate the translation-invariant p-adic Gibbs measures of Potts model on Cayley trees in terms of zeros of a certain polynomial. The translation-invariant p-adic Gibbs measures of Potts model on Cayley trees of order two and three was described with respect to some respective conditions on the coefficient of certain quadratic and cubic polynomials. In this paper, the set of p-adic Gibbs measures of p-adic Potts model on the Cayley tree of order four is considered. For this case, it is possible to associate the existence of the translation-invariant p-adic Gibbs measures with zeros of quartic polynomial over p-adic field.- Copyright
- © 2023 The Author(s)
- Open Access
- Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.
Cite this article
TY - CONF AU - Mohammad Azim Mohd Azahari AU - Mohd Ali Khameini Ahmad AU - Nor Muhainiah Mohd Ali PY - 2022 DA - 2022/12/12 TI - Translation-Invariant p-Adic Gibbs Measures for the Potts Model on the Cayley Tree of Order Four BT - Proceedings of the International Conference on Mathematical Sciences and Statistics 2022 (ICMSS 2022) PB - Atlantis Press SP - 24 EP - 33 SN - 2352-538X UR - https://doi.org/10.2991/978-94-6463-014-5_4 DO - 10.2991/978-94-6463-014-5_4 ID - Azahari2022 ER -