Statistics of geometric clusters in the Ising model on a Bethe lattice

The statistical mechanics method is developed for determination of generating function of like-sign spin clusters’ size distribution in Ising model as modification of Ising–Potts model by K. K. Murata (1979). It is applied to the ferromagnetic Ising model on Bethe lattice. The analytical results for...

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Bibliographic Details
Published in:Physica A 2019-08, Vol.527, p.121402, Article 121402
Main Author: Timonin, P.N.
Format: Article
Language:English
Subjects:
Like-sign Ising clusters
Percolation
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Summary:The statistical mechanics method is developed for determination of generating function of like-sign spin clusters’ size distribution in Ising model as modification of Ising–Potts model by K. K. Murata (1979). It is applied to the ferromagnetic Ising model on Bethe lattice. The analytical results for the field-temperature percolation phase diagram of + spin clusters and their size distribution are obtained. The last appears to be proportional to that of the classical non-correlated bond percolation with the bond probability, which depends on temperature and Ising model parameters. •New analytical representation for the generating function of the Ising like-sign clusters’ degrees distribution is found for arbitrary graph.•For ferromagnetic Ising model on a Bethe lattice we found the +spin clusters’ size distribution and percolation phase diagram.•The analytical representation would simplify the numerical calculations of the Ising like-sign clusters’ degrees distributions on Euclidean lattices.
ISSN:0378-4371
1873-2119
DOI:10.1016/j.physa.2019.121402