@article{TMF_2023_215_1_a7,
author = {M. M. Rahmatullaev and Zh. D. Dekhkonov},
title = {Potts model on {a~Cayley} tree: a~new class of {Gibbs} measures},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {150--162},
year = {2023},
volume = {215},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2023_215_1_a7/}
}
M. M. Rahmatullaev; Zh. D. Dekhkonov. Potts model on a Cayley tree: a new class of Gibbs measures. Teoretičeskaâ i matematičeskaâ fizika, Tome 215 (2023) no. 1, pp. 150-162. http://geodesic.mathdoc.fr/item/TMF_2023_215_1_a7/
[1] Kh.-O. Georgi, Gibbsovskie mery i fazovye perekhody, Mir, M., 1992 | MR | Zbl
[2] C. J. Preston, Gibbs States on Countable Sets, Cambridge Tracts in Mathematics, 68, Cambridge Univ. Press, Cambridge, 1974 | MR
[3] Ya. G. Sinai, Teoriya fazovykh perekhodov. Strogie rezultaty, Nauka, M., 1980 | MR | MR | Zbl
[4] N. N. Ganikhodzhaev, “O chistykh fazakh ferromagnitnoi modeli Pottsa s tremya sostoyaniyami na reshetke Bete vtorogo poryadka”, TMF, 85:2 (1990), 163–175 | DOI | MR
[5] N. N. Ganikhodjaev, U. A. Rozikov, “The Potts model with countable set of spin values on a Cayley tree”, Lett. Math. Phys., 75:2 (2006), 99–109 | DOI | MR
[6] U. A. Rozikov, R. M. Khakimov, “Periodicheskie mery Gibbsa dlya modeli Pottsa na dereve Keli”, TMF, 175:2 (2013), 300–312 | DOI | DOI | MR | Zbl
[7] R. M. Khakimov, “New periodic Gibbs measures for $q$-state Potts model on a Cayley tree”, Zhurn. SFU. Ser. Matem. i fiz., 7:3 (2014), 297–304, arXiv: 1406.0472
[8] C. Külske, U. A. Rozikov, R. M. Khakimov, “Description of translation-invariant splitting Gibbs measures for the Potts model on a Cayley tree”, J. Stat. Phys., 156:1 (2014), 189–200 | DOI | MR
[9] R. M. Khakimov, F. Kh. Khaidarov, “Translyatsionno-invariantnye i periodicheskie mery Gibbsa dlya modeli Pottsa na dereve Keli”, TMF, 189:2 (2016), 286–295 | DOI | DOI | MR
[10] U. A. Rozikov, “Gibbs measures of Potts model on Cayley trees: a survey and applications”, Rev. Math. Phys., 33:10 (2021), 2130007, 58 pp. | DOI | MR
[11] M. M. Rakhmatullaev, “Clabo periodicheskie mery Gibbsa i osnovnye sostoyaniya dlya modeli Pottsa s konkuriruyuschimi vzaimodeistviyami na dereve Keli”, TMF, 176:3 (2013), 477–493 | DOI | DOI | MR | Zbl
[12] M. M. Rahmatullaev, F. K. Rafikov, Sh. Kh. Azamov, “On constructive description of Gibbs measures for the Potts model on a Cayley tree”, Ukr. matem. zhurn., 73:7 (2021), 938–950 | DOI | DOI | MR
[13] Zh. D. Dekhkonov, “O $(k_0)$-translyatsionno-invariantnykh i $(k_0)$-periodicheskikh merakh Gibbsa dlya modeli Pottsa na dereve Keli”, Ufimsk. matem. zhurn., 14:4 (2022), 46–59 | MR
[14] M. M. Rakhmatullaev, “O slabo periodicheskikh merakh Gibbsa dlya modeli Pottsa s vneshnim polem na dereve Keli”, Ukr. matem. zhurn., 68:4 (2016), 529–541 | DOI
[15] M. M. Rahmatullaev, “Weakly periodic Gibbs measures of the Potts model with a special external field on a Cayley tree”, J. Math. Phys. Anal. Geom., 12:4 (2016), 302–314 | DOI | MR
[16] M. M. Rakhmatullaev, “Suschestvovanie slabo periodicheskikh mer Gibbsa dlya modeli Pottsa na dereve Keli”, TMF, 180:3 (2014), 307–317 | DOI | DOI | MR
[17] R. M. Khakimov, M. T. Makhammadaliev, “Translyatsionnaya invariantnost periodicheskikh mer Gibbsa dlya modeli Pottsa na dereve Keli”, TMF, 199:2 (2019), 291–301 | DOI | DOI | MR
[18] U. A. Rozikov, M. M. Rakhmatullaev, R. M. Khakimov, “Periodicheskie mery Gibbsa dlya modeli Pottsa s translyatsionno-invariantnym i periodicheskim vneshnimi polyami na dereve Keli”, TMF, 210:1 (2022), 156–176 | DOI | DOI
[19] U. A. Rozikov, M. M. Rahmatullaev, “Ising model on Cayley trees: a new class of Gibbs measures and their comparison with known ones”, J. Stat. Mech., 2017:9 (2017), 093205, 15 pp. | DOI | MR
[20] U. A. Rozikov, Gibbs Measures on Cayley Trees, World Sci., Singapore, 2013 | DOI | MR
[21] H. Akin, U. A. Rozikov, S. Temir, “A new set of limiting Gibbs measures for the Ising model on a Cayley tree”, J. Stat. Phys., 142:2 (2011), 314–321 | DOI | MR