A dynamical system approach to phase transitions for p-adic Potts model on the Cayley tree of order two
In the present paper, we introduce a new kind of p-adic measures for (q + 1)-state Potts model, called generalized p-adic quasi Gibbs measure. For such a model, we derive a recursive relations with respect to boundary conditions. We employ a dynamical system approach to establish phase transition ph...
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| Format: | Article |
| Language: | en |
| Published: |
Elsevier
2012
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| Online Access: | http://irep.iium.edu.my/28682/1/mf-ROMP%282012%29.pdf http://irep.iium.edu.my/28682/ http://dx.doi.org/10.1016/S0034-4877(12)60053-6 |
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| Summary: | In the present paper, we introduce a new kind of p-adic measures for (q + 1)-state Potts model, called generalized p-adic quasi Gibbs measure. For such a model, we derive a recursive relations with respect to boundary conditions. We employ a dynamical system approach to establish phase transition phenomena for the given model. Namely, using the derived recursive relations we define a one-dimensional fractional p-adic dynamical system. We show that if q is
divisible by p, then such a dynamical system has two repelling and one attractive fixed points. In this case, there exists a strong phase transition. If q is not divisible by p, then the fixed points are neutral, and this yields the existence of a quasi phase transition. |
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