On Dynamical Systems and Phase Transitions for q + 1-state p-adic Potts Model on the Cayley Tree
Abstract In the present paper, we study a new kind of p-adic measures for q + 1-state Potts model, called p-adic quasi Gibbs measure. For such a model, we derive a recursive relations with respect to boundary conditions. Note that we consider two mode of interactions: ferromagnetic and antiferromagn...
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| Autor*in: |
Mukhamedov, Farrukh [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2012 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Science+Business Media B.V. 2012 |
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| Übergeordnetes Werk: |
Enthalten in: Mathematical physics, analysis and geometry - Springer Netherlands, 1998, 16(2012), 1 vom: 19. Sept., Seite 49-87 |
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| Übergeordnetes Werk: |
volume:16 ; year:2012 ; number:1 ; day:19 ; month:09 ; pages:49-87 |
| Links: |
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| DOI / URN: |
10.1007/s11040-012-9120-z |
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OLC2047962528 |
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| 520 | |a Abstract In the present paper, we study a new kind of p-adic measures for q + 1-state Potts model, called p-adic quasi Gibbs measure. For such a model, we derive a recursive relations with respect to boundary conditions. Note that we consider two mode of interactions: ferromagnetic and antiferromagnetic. In both cases, we investigate a phase transition phenomena from the associated dynamical system point of view. Namely, using the derived recursive relations we define a fractional p-adic dynamical system. In ferromagnetic case, we establish that if q is divisible by p, then such a dynamical system has two repelling and one attractive fixed points. We find basin of attraction of the fixed point. This allows us to describe all solutions of the nonlinear recursive equations. Moreover, in that case there exists the strong phase transition. If q is not divisible by p, then the fixed points are neutral, and this yields that the existence of the quasi phase transition. In antiferromagnetic case, there are two attractive fixed points, and we find basins of attraction of both fixed points, and describe solutions of the nonlinear recursive equation. In this case, we prove the existence of a quasi phase transition. | ||
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10.1007/s11040-012-9120-z doi (DE-627)OLC2047962528 (DE-He213)s11040-012-9120-z-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn 31.40$jAnalysis: Allgemeines bkl 31.50$jGeometrie: Allgemeines bkl 33.06$jMathematische Methoden der Physik bkl Mukhamedov, Farrukh verfasserin aut On Dynamical Systems and Phase Transitions for q + 1-state p-adic Potts Model on the Cayley Tree 2012 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media B.V. 2012 Abstract In the present paper, we study a new kind of p-adic measures for q + 1-state Potts model, called p-adic quasi Gibbs measure. For such a model, we derive a recursive relations with respect to boundary conditions. Note that we consider two mode of interactions: ferromagnetic and antiferromagnetic. In both cases, we investigate a phase transition phenomena from the associated dynamical system point of view. Namely, using the derived recursive relations we define a fractional p-adic dynamical system. In ferromagnetic case, we establish that if q is divisible by p, then such a dynamical system has two repelling and one attractive fixed points. We find basin of attraction of the fixed point. This allows us to describe all solutions of the nonlinear recursive equations. Moreover, in that case there exists the strong phase transition. If q is not divisible by p, then the fixed points are neutral, and this yields that the existence of the quasi phase transition. In antiferromagnetic case, there are two attractive fixed points, and we find basins of attraction of both fixed points, and describe solutions of the nonlinear recursive equation. In this case, we prove the existence of a quasi phase transition. -adic numbers Potts model -adic quasi Gibbs measure Phase transition Enthalten in Mathematical physics, analysis and geometry Springer Netherlands, 1998 16(2012), 1 vom: 19. Sept., Seite 49-87 (DE-627)300830831 (DE-600)1484000-5 (DE-576)091204909 1385-0172 nnns volume:16 year:2012 number:1 day:19 month:09 pages:49-87 https://doi.org/10.1007/s11040-012-9120-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_2002 31.40$jAnalysis: Allgemeines VZ 106423258 (DE-625)106423258 31.50$jGeometrie: Allgemeines VZ 106408127 (DE-625)106408127 33.06$jMathematische Methoden der Physik VZ 106407937 (DE-625)106407937 AR 16 2012 1 19 09 49-87 |
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Mukhamedov, Farrukh |
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On Dynamical Systems and Phase Transitions for q + 1-state p-adic Potts Model on the Cayley Tree |
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Abstract In the present paper, we study a new kind of p-adic measures for q + 1-state Potts model, called p-adic quasi Gibbs measure. For such a model, we derive a recursive relations with respect to boundary conditions. Note that we consider two mode of interactions: ferromagnetic and antiferromagnetic. In both cases, we investigate a phase transition phenomena from the associated dynamical system point of view. Namely, using the derived recursive relations we define a fractional p-adic dynamical system. In ferromagnetic case, we establish that if q is divisible by p, then such a dynamical system has two repelling and one attractive fixed points. We find basin of attraction of the fixed point. This allows us to describe all solutions of the nonlinear recursive equations. Moreover, in that case there exists the strong phase transition. If q is not divisible by p, then the fixed points are neutral, and this yields that the existence of the quasi phase transition. In antiferromagnetic case, there are two attractive fixed points, and we find basins of attraction of both fixed points, and describe solutions of the nonlinear recursive equation. In this case, we prove the existence of a quasi phase transition. © Springer Science+Business Media B.V. 2012 |
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Abstract In the present paper, we study a new kind of p-adic measures for q + 1-state Potts model, called p-adic quasi Gibbs measure. For such a model, we derive a recursive relations with respect to boundary conditions. Note that we consider two mode of interactions: ferromagnetic and antiferromagnetic. In both cases, we investigate a phase transition phenomena from the associated dynamical system point of view. Namely, using the derived recursive relations we define a fractional p-adic dynamical system. In ferromagnetic case, we establish that if q is divisible by p, then such a dynamical system has two repelling and one attractive fixed points. We find basin of attraction of the fixed point. This allows us to describe all solutions of the nonlinear recursive equations. Moreover, in that case there exists the strong phase transition. If q is not divisible by p, then the fixed points are neutral, and this yields that the existence of the quasi phase transition. In antiferromagnetic case, there are two attractive fixed points, and we find basins of attraction of both fixed points, and describe solutions of the nonlinear recursive equation. In this case, we prove the existence of a quasi phase transition. © Springer Science+Business Media B.V. 2012 |
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Abstract In the present paper, we study a new kind of p-adic measures for q + 1-state Potts model, called p-adic quasi Gibbs measure. For such a model, we derive a recursive relations with respect to boundary conditions. Note that we consider two mode of interactions: ferromagnetic and antiferromagnetic. In both cases, we investigate a phase transition phenomena from the associated dynamical system point of view. Namely, using the derived recursive relations we define a fractional p-adic dynamical system. In ferromagnetic case, we establish that if q is divisible by p, then such a dynamical system has two repelling and one attractive fixed points. We find basin of attraction of the fixed point. This allows us to describe all solutions of the nonlinear recursive equations. Moreover, in that case there exists the strong phase transition. If q is not divisible by p, then the fixed points are neutral, and this yields that the existence of the quasi phase transition. In antiferromagnetic case, there are two attractive fixed points, and we find basins of attraction of both fixed points, and describe solutions of the nonlinear recursive equation. In this case, we prove the existence of a quasi phase transition. © Springer Science+Business Media B.V. 2012 |
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