On contour arguments for the three state Potts model with competing interactions on a semi-infinite Cayley tree

Farrukh Mukhamedov; Utkir Rozikov; José F.F. Mendes

doi:10.1063/1.2408398

On contour arguments for the three state Potts model with competing interactions on a semi-infinite Cayley tree

Farrukh Mukhamedov
, Utkir Rozikov
, José F.F. Mendes

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

15 Citations (Scopus)

Abstract

We consider the Potts model with competing two-step interactions and spin values 1, 2, 3 on a semi-infinite Cayley tree of order 2. We describe ground states and verify the Peierls condition for the model. Using a contour argument we show the existence of three different Gibbs measures associated with translation invariant ground states.

Original language	English
Article number	013301
Journal	Journal of Mathematical Physics
Volume	48
Issue number	1
DOIs	https://doi.org/10.1063/1.2408398
Publication status	Published - 2007
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1063/1.2408398

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title = "On contour arguments for the three state Potts model with competing interactions on a semi-infinite Cayley tree",

abstract = "We consider the Potts model with competing two-step interactions and spin values 1, 2, 3 on a semi-infinite Cayley tree of order 2. We describe ground states and verify the Peierls condition for the model. Using a contour argument we show the existence of three different Gibbs measures associated with translation invariant ground states.",

author = "Farrukh Mukhamedov and Utkir Rozikov and Mendes, \{Jos{\'e} F.F.\}",

note = "Funding Information: One of the authors (F.M.) thanks the FCT (Portugal) grant SFRH∕BPD∕17419∕2004. Another author (J.F.F.M.) acknowledges projects POCTI∕FAT∕46241∕2002, POCTI∕MAT∕46176∕2002, and European research NEST project DYSONET∕012911. Another author (U.R.) thanks the NATO Reintegration Grant FEL. RIG. 980771, and Grants ΦM.1.152, Φ.1.1.2 and Φ.2.1.56 of CST of the Republic Uzbekistan. He also acknowledges the ICTP for providing financial support and all facilities. The final part of this work was done, when he was the Junior Associate at the ICTP, Trieste.",

year = "2007",

doi = "10.1063/1.2408398",

language = "English",

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AU - Rozikov, Utkir

AU - Mendes, José F.F.

N1 - Funding Information: One of the authors (F.M.) thanks the FCT (Portugal) grant SFRH∕BPD∕17419∕2004. Another author (J.F.F.M.) acknowledges projects POCTI∕FAT∕46241∕2002, POCTI∕MAT∕46176∕2002, and European research NEST project DYSONET∕012911. Another author (U.R.) thanks the NATO Reintegration Grant FEL. RIG. 980771, and Grants ΦM.1.152, Φ.1.1.2 and Φ.2.1.56 of CST of the Republic Uzbekistan. He also acknowledges the ICTP for providing financial support and all facilities. The final part of this work was done, when he was the Junior Associate at the ICTP, Trieste.

PY - 2007

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On contour arguments for the three state Potts model with competing interactions on a semi-infinite Cayley tree

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