Geodesic
Periodic and weakly periodic ground states for the Potts model with competing interactions on the Cayley tree
Matematičeskie trudy, Tome 18 (2015) no. 2, pp. 112-132.

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We consider the Potts model with competing interactions on the Cayley tree of order $k$ with $k\geq 2$. We describe the sets of periodic and weakly periodic ground states corresponding to normal subgroups of the group representation of the Cayley tree of index $4$. 
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M. A. Rasulova; M. M. Rahmatullaev. Periodic and weakly periodic ground states for the Potts model with competing interactions on the Cayley tree. Matematičeskie trudy, Tome 18 (2015) no. 2, pp. 112-132. http://geodesic.mathdoc.fr/item/MT_2015_18_2_a6/

[1] Botirov G. I., Rozikov U. A., “Model Pottsa s konkuriruyuschimi vzaimodeistviyami na dereve Keli: konturnyi metod”, TMF, 153:1 (2007), 86–97 | DOI | Zbl

[2] Ganikhodzhaev N. N., “Gruppovoe predstavlenie i avtomorfizmy dereva Keli”, Dokl. AN RUz., 1994, no. 4, 3–5

[3] Emelichev V. A., Melnikov O. I., Sarvanov V. I., Tyshkevich R. I., Lektsii po teorii grafov, Nauka, M., 1990

[4] Kargapolov M. I., Merzlyakov Yu. I., Osnovy teorii grupp, Nauka, M., 1982

[5] Rakhmatullaev M. M., “Slabo periodicheskie mery Gibbsa i osnovnye sostoyaniya dlya modeli Pottsa s konkuriruyuschimi vzaimodeistviyami na dereve Keli”, TMF, 176:3 (2013), 477–493 | DOI | Zbl

[6] Rakhmatullaev M. M., Rasulova M. A., “Suschestvovanie slabo periodicheskikh osnovnykh sostoyanii dlya modeli Pottsa s konkuriruyuschimi vzaimodeistviyami na dereve Keli”, Dokl. AN RUz., 2013, no. 3, 10–13

[7] Rozikov U. A., Rakhmatullaev M. M., “Slabo periodicheskie osnovnye sostoyaniya i mery Gibbsa dlya modeli Izinga s konkuriruyuschimi vzaimodeistviyami na dereve Keli”, TMF, 160:3 (2009), 507–516 | DOI | Zbl

[8] Sinai Ya. G., Teoriya fazovykh perekhodov. Strogie rezultaty, Nauka, M., 1980

[9] Minlos R. A., Introduction to Mathematical Statistical Physics, University Lecture Series, 19, American Mathematical Society, Providence, RI, 2000 | Zbl

[10] Rahmatullaev M. M., “Description of weak periodic ground states of Ising model with competing interactions on Cayley tree”, Appl. Math. Inf. Sci., 4:2 (2010), 237–241

[11] Rozikov U. A., Gibbs Measures on Cayley Trees, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2013 | Zbl