Phase diagram of the three states Potts model with next nearest neighbour interactions on the Bethe lattice

Nasir Ganikhodjaev; Farrukh Mukhamedov; Chin Hee Pah

doi:10.1016/j.physleta.2008.10.060

Phase diagram of the three states Potts model with next nearest neighbour interactions on the Bethe lattice

Nasir Ganikhodjaev, Farrukh Mukhamedov, Chin Hee Pah

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

31 Citations (Scopus)

Abstract

We have found an exact phase diagram of the Potts model with competing nearest neighbor and next nearest neighbor interactions on the Bethe lattice of order two. The diagram consists of five phases: ferromagnetic, paramagnetic, modulated, antiphase and paramodulated, all meeting at the multicritical point (T = 0, p = 1 / 3). We report on a new phase which we denote as paramodulated, found at low temperatures and characterized by zero average magnetization lying inside the modulated phase. Such a phase, inherent in the Potts model has no analogues in the Ising setting.

Original language	English
Pages (from-to)	33-38
Number of pages	6
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	373
Issue number	1
DOIs	https://doi.org/10.1016/j.physleta.2008.10.060
Publication status	Published - Dec 22 2008
Externally published	Yes

Keywords

Bethe lattice
Dynamical system
Modulated phase
Next nearest neighbour
Phase diagram
Potts model

ASJC Scopus subject areas

General Physics and Astronomy

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10.1016/j.physleta.2008.10.060

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title = "Phase diagram of the three states Potts model with next nearest neighbour interactions on the Bethe lattice",

abstract = "We have found an exact phase diagram of the Potts model with competing nearest neighbor and next nearest neighbor interactions on the Bethe lattice of order two. The diagram consists of five phases: ferromagnetic, paramagnetic, modulated, antiphase and paramodulated, all meeting at the multicritical point (T = 0, p = 1 / 3). We report on a new phase which we denote as paramodulated, found at low temperatures and characterized by zero average magnetization lying inside the modulated phase. Such a phase, inherent in the Potts model has no analogues in the Ising setting.",

keywords = "Bethe lattice, Dynamical system, Modulated phase, Next nearest neighbour, Phase diagram, Potts model",

author = "Nasir Ganikhodjaev and Farrukh Mukhamedov and Pah, {Chin Hee}",

note = "Funding Information: This work was partially supported by SAGA Fund P77c by the Ministry of Science, Technology and Innovation (MOSTI) through the Academy of Sciences Malaysia (ASM). The authors thank the referee for his essential remarks.",

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T1 - Phase diagram of the three states Potts model with next nearest neighbour interactions on the Bethe lattice

AU - Ganikhodjaev, Nasir

AU - Mukhamedov, Farrukh

AU - Pah, Chin Hee

N1 - Funding Information: This work was partially supported by SAGA Fund P77c by the Ministry of Science, Technology and Innovation (MOSTI) through the Academy of Sciences Malaysia (ASM). The authors thank the referee for his essential remarks.

PY - 2008/12/22

Y1 - 2008/12/22

N2 - We have found an exact phase diagram of the Potts model with competing nearest neighbor and next nearest neighbor interactions on the Bethe lattice of order two. The diagram consists of five phases: ferromagnetic, paramagnetic, modulated, antiphase and paramodulated, all meeting at the multicritical point (T = 0, p = 1 / 3). We report on a new phase which we denote as paramodulated, found at low temperatures and characterized by zero average magnetization lying inside the modulated phase. Such a phase, inherent in the Potts model has no analogues in the Ising setting.

AB - We have found an exact phase diagram of the Potts model with competing nearest neighbor and next nearest neighbor interactions on the Bethe lattice of order two. The diagram consists of five phases: ferromagnetic, paramagnetic, modulated, antiphase and paramodulated, all meeting at the multicritical point (T = 0, p = 1 / 3). We report on a new phase which we denote as paramodulated, found at low temperatures and characterized by zero average magnetization lying inside the modulated phase. Such a phase, inherent in the Potts model has no analogues in the Ising setting.

KW - Bethe lattice

KW - Dynamical system

KW - Modulated phase

KW - Next nearest neighbour

KW - Phase diagram

KW - Potts model

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Phase diagram of the three states Potts model with next nearest neighbour interactions on the Bethe lattice

Abstract

Keywords

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