On the existence of phase transition for the 1D p-adic countable state Potts model

F. M. Mukhamedov

doi:10.1134/S0001434615070305

On the existence of phase transition for the 1D p-adic countable state Potts model

Research output: Contribution to journal › Article › peer-review

Abstract

In the present paper we establish the existence of a phase transition for one-dimensional the countable state p-adic Potts model. To establish such results, we investigate an infinite dimensional nonlinear p-adic operator associated with the model. It turns out that the finding condition does not depend on values of the prime p, and therefore, an analogous fact is not true when the number of spins is finite.

Original language	English
Pages (from-to)	283-288
Number of pages	6
Journal	Mathematical Notes
Volume	98
Issue number	1-2
DOIs	https://doi.org/10.1134/S0001434615070305
Publication status	Published - Jul 28 2015
Externally published	Yes

Keywords

Cayley tree
countable state
Gibbs measure
Markov process
p-adic numbers
phase transition
Potts model

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1134/S0001434615070305

Cite this

@article{a2b85488893b4e3eba6feab6d2631533,

title = "On the existence of phase transition for the 1D p-adic countable state Potts model",

abstract = "In the present paper we establish the existence of a phase transition for one-dimensional the countable state p-adic Potts model. To establish such results, we investigate an infinite dimensional nonlinear p-adic operator associated with the model. It turns out that the finding condition does not depend on values of the prime p, and therefore, an analogous fact is not true when the number of spins is finite.",

keywords = "Cayley tree, countable state, Gibbs measure, Markov process, p-adic numbers, phase transition, Potts model",

author = "Mukhamedov, {F. M.}",

note = "Publisher Copyright: {\textcopyright} 2015, Pleiades Publishing, Ltd.",

year = "2015",

month = jul,

day = "28",

doi = "10.1134/S0001434615070305",

language = "English",

volume = "98",

pages = "283--288",

journal = "Mathematical Notes of the Academy of Sciences of the USSR",

issn = "1757-7489",

publisher = "Springer Science + Business Media",

number = "1-2",

}

TY - JOUR

T1 - On the existence of phase transition for the 1D p-adic countable state Potts model

AU - Mukhamedov, F. M.

PY - 2015/7/28

Y1 - 2015/7/28

N2 - In the present paper we establish the existence of a phase transition for one-dimensional the countable state p-adic Potts model. To establish such results, we investigate an infinite dimensional nonlinear p-adic operator associated with the model. It turns out that the finding condition does not depend on values of the prime p, and therefore, an analogous fact is not true when the number of spins is finite.

AB - In the present paper we establish the existence of a phase transition for one-dimensional the countable state p-adic Potts model. To establish such results, we investigate an infinite dimensional nonlinear p-adic operator associated with the model. It turns out that the finding condition does not depend on values of the prime p, and therefore, an analogous fact is not true when the number of spins is finite.

KW - Cayley tree

KW - countable state

KW - Gibbs measure

KW - Markov process

KW - p-adic numbers

KW - phase transition

KW - Potts model

UR - http://www.scopus.com/inward/record.url?scp=84940103266&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84940103266&partnerID=8YFLogxK

U2 - 10.1134/S0001434615070305

DO - 10.1134/S0001434615070305

M3 - Article

AN - SCOPUS:84940103266

SN - 1757-7489

VL - 98

SP - 283

EP - 288

JO - Mathematical Notes of the Academy of Sciences of the USSR

JF - Mathematical Notes of the Academy of Sciences of the USSR

IS - 1-2

ER -

On the existence of phase transition for the 1D p-adic countable state Potts model

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this