Phase transitions for p-adic Potts model on the Cayley tree of order three
In the present paper, we study a phase transition problem for the q-state p-adic Potts model over the Cayley tree of order three. We consider a more general notion of p-adic Gibbs measure which depends on parameter ρ∈Qp. Such a measure is called generalized p-adic quasi Gibbs measure. When ρ equals...
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Institute of Physics Publishing Ltd.
2013
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iium-317452013-09-24T05:20:06Z http://irep.iium.edu.my/31745/ Phase transitions for p-adic Potts model on the Cayley tree of order three Mukhamedov, Farrukh Akin, Hasan QA Mathematics QC Physics In the present paper, we study a phase transition problem for the q-state p-adic Potts model over the Cayley tree of order three. We consider a more general notion of p-adic Gibbs measure which depends on parameter ρ∈Qp. Such a measure is called generalized p-adic quasi Gibbs measure. When ρ equals the p-adic exponent, then it coincides with the p-adic Gibbs measure. When ρ = p, then it coincides with the p-adic quasi Gibbs measure. Therefore, we investigate two regimes with respect to the value of |ρ|p. Namely, in the first regime, one takes ρ = expp(J) for some J∈Qp, in the second one |ρ|p < 1. In each regime, we first find conditions for the existence of generalized p-adic quasi Gibbs measures. Furthermore, in the first regime, we establish the existence of the phase transition under some conditions. In the second regime, when |ρ|p,|q|p ≤ p−2 we prove the existence of a quasi phase transition. It turns out that if $\vert \rho \vert _{p}\lt \vert q-1\vert _{p}^{2}\lt 1$ and $\sqrt{-3}\in {\mathbb{Q}}_{p}$, then one finds the existence of the strong phase transition. Institute of Physics Publishing Ltd. 2013-07 Article PeerReviewed application/pdf en http://irep.iium.edu.my/31745/1/mfha-JSTAT%282013%29.pdf Mukhamedov, Farrukh and Akin, Hasan (2013) Phase transitions for p-adic Potts model on the Cayley tree of order three. Journal of Statistical Mechanics: Theory and Experiment, 2013 (07). P07014 (1)-P07014 (30). ISSN 1742-5468 (O) http://iopscience.iop.org/1742-5468/2013/07/P07014 10.1088/1742-5468/2013/07/P07014 |
| repository_type |
Digital Repository |
| institution_category |
Local University |
| institution |
International Islamic University Malaysia |
| building |
IIUM Repository |
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Online Access |
| language |
English |
| topic |
QA Mathematics QC Physics |
| spellingShingle |
QA Mathematics QC Physics Mukhamedov, Farrukh Akin, Hasan Phase transitions for p-adic Potts model on the Cayley tree of order three |
| description |
In the present paper, we study a phase transition problem for the q-state p-adic Potts model over the Cayley tree of order three. We consider a more general notion of p-adic Gibbs measure which depends on parameter ρ∈Qp. Such a measure is called generalized p-adic quasi Gibbs measure. When ρ equals the p-adic exponent, then it coincides with the p-adic Gibbs measure. When ρ = p, then it coincides with the p-adic quasi Gibbs measure. Therefore, we investigate two regimes with respect to the value of |ρ|p. Namely, in the first regime, one takes ρ = expp(J) for some J∈Qp, in the second one |ρ|p < 1. In each regime, we first find conditions for the existence of generalized p-adic quasi Gibbs measures. Furthermore, in the first regime, we establish the existence of the phase transition under some conditions. In the second regime, when |ρ|p,|q|p ≤ p−2 we prove the existence of a quasi phase transition. It turns out that if $\vert \rho \vert _{p}\lt \vert q-1\vert _{p}^{2}\lt 1$ and $\sqrt{-3}\in {\mathbb{Q}}_{p}$, then one finds the existence of the strong phase transition. |
| format |
Article |
| author |
Mukhamedov, Farrukh Akin, Hasan |
| author_facet |
Mukhamedov, Farrukh Akin, Hasan |
| author_sort |
Mukhamedov, Farrukh |
| title |
Phase transitions for p-adic Potts model on the Cayley tree of order three |
| title_short |
Phase transitions for p-adic Potts model on the Cayley tree of order three |
| title_full |
Phase transitions for p-adic Potts model on the Cayley tree of order three |
| title_fullStr |
Phase transitions for p-adic Potts model on the Cayley tree of order three |
| title_full_unstemmed |
Phase transitions for p-adic Potts model on the Cayley tree of order three |
| title_sort |
phase transitions for p-adic potts model on the cayley tree of order three |
| publisher |
Institute of Physics Publishing Ltd. |
| publishDate |
2013 |
| url |
http://irep.iium.edu.my/31745/ http://irep.iium.edu.my/31745/ http://irep.iium.edu.my/31745/ http://irep.iium.edu.my/31745/1/mfha-JSTAT%282013%29.pdf |
| first_indexed |
2023-09-18T20:45:53Z |
| last_indexed |
2023-09-18T20:45:53Z |
| _version_ |
1777409671782465536 |