Geodesic
Weakly periodic ground states and Gibbs measures for the~Ising model with competing interactions on the~Cayley tree
Teoretičeskaâ i matematičeskaâ fizika, Tome 160 (2009) no. 3, pp. 507-516

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We introduce the notion of a weakly periodic configuration. For the Ising model with competing interactions, we describe the set of all weakly periodic ground states corresponding to normal divisors of indices $2$ and $4$ of the group representation of the Cayley tree. In addition, we study new Gibbs measures for the Ising model.
Keywords: Cayley tree, Gibbs measure, Ising model, weakly periodic ground state. 
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     author = {U. A. Rozikov and M. M. Rakhmatullaev},
     title = {Weakly periodic ground states and {Gibbs} measures for {the~Ising} model with competing interactions on {the~Cayley} tree},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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U. A. Rozikov; M. M. Rakhmatullaev. Weakly periodic ground states and Gibbs measures for the~Ising model with competing interactions on the~Cayley tree. Teoretičeskaâ i matematičeskaâ fizika, Tome 160 (2009) no. 3, pp. 507-516. http://geodesic.mathdoc.fr/item/TMF_2009_160_3_a5/