najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2022-13-5-498-502najo-261Research ArticleСтатьиPhase transitions for the "uncle-nephew" modelGanikhodjaevN. N.nasirgani@yandex.comRahmatullaevM. M.mrahmatullaev@rambler.ruAbdusalomovaM. R.mahliyo13abdusalomova@gmail.comInstitute of MathematicsRussian FederationInstitute of Mathematics; Namangan State UniversityRussian FederationNamangan State UniversityRussian Federation202206062025135498502Copyright © Ganikhodjaev N.N., Rahmatullaev M.M., Abdusalomova M.R., 20252025Ganikhodjaev N.N., Rahmatullaev M.M., Abdusalomova M.R.Ganikhodjaev N.N., Rahmatullaev M.M., Abdusalomova M.R.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/261

We investigate a problem of phase transition for all possible phases of "uncle-nephew" model on the semi-infinite Cayley tree of second order. It is proved that one can reach the phase transition for this model only in the class of ferromagnetic phase.

Cayley treeIsing modelphase transitionperiodic Gibbs measuresfamily treeReferencesVannimenus J. Modulated phase of an Ising system with competing interactions on a Cayley tree. Z Phys B., 1981, 43, P. 141-148.Vannimenus J. Modulated phase of an Ising system with competing interactions on a Cayley tree. Z Phys B., 1981, 43, P. 141-148.Mariz A.M., Tsallis C., Albuquerque E.L. Phase diagram of the Ising model on a Cayley tree in the presence of competing interactions and magnetic field. J Stat Phys., 1985, 40, P. 577-592.Mariz A.M., Tsallis C., Albuquerque E.L. Phase diagram of the Ising model on a Cayley tree in the presence of competing interactions and magnetic field. J Stat Phys., 1985, 40, P. 577-592.da Silva C.R., Countinho C. Ising model on the Bethe lattice with competing interactions up to the third-nearest-neighbor generations. Phys Rev B., 1986, 34, P. 7975-7985.da Silva C.R., Countinho C. Ising model on the Bethe lattice with competing interactions up to the third-nearest-neighbor generations. Phys Rev B., 1986, 34, P. 7975-7985.Inavarisho S., Thompson C.J.Compting Ising interactions and chaotic glass-like behaviour on a Cayley tree. Phys Lett A., 1983, 97, P. 245-248.Inavarisho S., Thompson C.J.Compting Ising interactions and chaotic glass-like behaviour on a Cayley tree. Phys Lett A., 1983, 97, P. 245-248.Inawashiro S., Thompson C.J., Honda G. Ising model with competing interactions on a Cayley tree. J Stat Phys., 1983, 33, P. 419-436.Inawashiro S., Thompson C.J., Honda G. Ising model with competing interactions on a Cayley tree. J Stat Phys., 1983, 33, P. 419-436.Yokio C.S.O., de Oliviera M.J., Salinas S.R. Strange attractor in the Ising model with competing interaction on the Cayley tree. Phys Rev Lett., 1995, 54, P. 163-166.Yokio C.S.O., de Oliviera M.J., Salinas S.R. Strange attractor in the Ising model with competing interaction on the Cayley tree. Phys Rev Lett., 1995, 54, P. 163-166.Thompson C.J. On mean field equations for spin glasses. J Stat Phys., 1982, 27, P. 457-472.Thompson C.J. On mean field equations for spin glasses. J Stat Phys., 1982, 27, P. 457-472.Ganikhodjaev N., Rodzhan M.H.M. Ising Model on the Cayley tree with competing interactions up to the third nearest-neighbors with spins belonging to different branches of the tree. J Kor Phys Soc., 2015, 66, P. 1200-1206.Ganikhodjaev N., Rodzhan M.H.M. Ising Model on the Cayley tree with competing interactions up to the third nearest-neighbors with spins belonging to different branches of the tree. J Kor Phys Soc., 2015, 66, P. 1200-1206.Ganikhodjaev N.N., Ising model with competing uncle-nephew interactions. Phase Transitions, 2019, 92(8), P. 730-736.Ganikhodjaev N.N., Ising model with competing uncle-nephew interactions. Phase Transitions, 2019, 92(8), P. 730-736.

The authors declare that there are no conflicts of interest present.