Geodesic
On the Existence of Generalized Gibbs Measures for the One-Dimensional $p$-adic Countable State Potts Model
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Selected topics of mathematical physics and $p$-adic analysis, Tome 265 (2009), pp. 177-188

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We consider the one-dimensional countable state $p$-adic Potts model. A construction of generalized $p$-adic Gibbs measures depending on weights $\lambda$ is given, and an investigation of such measures is reduced to the examination of a $p$-adic dynamical system. This dynamical system has a form of series of rational functions. Studying such a dynamical system, under some condition concerning weights, we prove the existence of generalized $p$-adic Gibbs measures. Note that the condition found does not depend on the values of the prime $p$, and therefore an analogous fact is not true when the number of states is finite. It is also shown that under the condition there may occur a phase transition. 
@article{TM_2009_265_a15,
     author = {F. Mukhamedov},
     title = {On the {Existence} of {Generalized} {Gibbs} {Measures} for the {One-Dimensional} $p$-adic {Countable} {State} {Potts} {Model}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {177--188},
     publisher = {mathdoc},
     volume = {265},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TM_2009_265_a15/}
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F. Mukhamedov. On the Existence of Generalized Gibbs Measures for the One-Dimensional $p$-adic Countable State Potts Model. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Selected topics of mathematical physics and $p$-adic analysis, Tome 265 (2009), pp. 177-188. http://geodesic.mathdoc.fr/item/TM_2009_265_a15/