Voir la notice de l'article provenant de la source Math-Net.Ru
@article{JSFU_2022_15_2_a2, author = {Muzaffar M. Rahmatullaev and Bunyod U. Abraev}, title = {On ground states for the {SOS} model with competing interactions}, journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika}, pages = {162--175}, publisher = {mathdoc}, volume = {15}, number = {2}, year = {2022}, language = {en}, url = {http://geodesic.mathdoc.fr/item/JSFU_2022_15_2_a2/} }
TY - JOUR AU - Muzaffar M. Rahmatullaev AU - Bunyod U. Abraev TI - On ground states for the SOS model with competing interactions JO - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika PY - 2022 SP - 162 EP - 175 VL - 15 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/JSFU_2022_15_2_a2/ LA - en ID - JSFU_2022_15_2_a2 ER -
%0 Journal Article %A Muzaffar M. Rahmatullaev %A Bunyod U. Abraev %T On ground states for the SOS model with competing interactions %J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika %D 2022 %P 162-175 %V 15 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/JSFU_2022_15_2_a2/ %G en %F JSFU_2022_15_2_a2
Muzaffar M. Rahmatullaev; Bunyod U. Abraev. On ground states for the SOS model with competing interactions. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 2, pp. 162-175. http://geodesic.mathdoc.fr/item/JSFU_2022_15_2_a2/
[1] M.M. Rakhmatullaev, “Description of weak periodic ground states of Ising model with competing interactions on Cayley tree”, Appl. Math. Inf. Sci., 4 (2010), 237 | MR | Zbl
[2] R. Fernandez, Contour ensembles and the description of Gibbsian probability distri-butions at low temperature, 1998 | MR
[3] G.I. Botirov, U.A. Rozikov, “Potts model with competing interactions on the Cayley tree: The contour method”, Theoret. Math. Phys., 153 (2007), 1423 | DOI | MR | Zbl
[4] U.A. Rozikov, Gibbs Measures on Cayley Trees, World Scientific, Haversack, 2013 | MR | Zbl
[5] U.A. Rozikov, M.M. Rakhmatullaev, “Weakly periodic ground states and Gibbs measures for the Ising model with competing interactions on the Cayley tree”, Theoret. Math. Phys., 160 (2009), 1292 | DOI | MR | Zbl
[6] M.M. Rakhmatullaev, “Weakly periodic Gibbs measures and ground states for the Potts model with competing interactions on the Cayley tree”, Theoret. Math. Phys., 176 (2013), 1236 | DOI | MR | Zbl
[7] M.M. Rakhmatullaev, M.A. Rasulova, “Existence of weakly periodic ground states for the Potts model with competing interactions on the Cayley tree”, Dokl. Akad. nauk Resp. Uzbekistan, 10:3 (2013) (in Russian) | MR
[8] M.M. Rahmatullaev, M.A. Rasulova, “Periodic and Weakly Periodic Ground States for the Potts Model with Competing Interactions on the Cayley Tree”, Siberian Advances in Mathematics, 26:3 (2016), 215–229 | DOI | MR
[9] U.A. Rozikov, “A Constructive Description of Ground States and Gibbs Measures for Ising Model with Two-Step Interactions on Cayley Tree”, Jurnal of Statistical Physics, 122:2 (2006), 217–235 | DOI | MR | Zbl
[10] G.I Botirov, M.M. Rahmatullaev, “Ground states for Potts model with a countable set of spin values on a Cayley tree”, Algebra, complex analysis, and pluripotential theory, Springer Proc. Math. Stat., 264, 2018, 59–71 | MR | Zbl
[11] U.A. Rozikov, “A contour method on Cayley trees”, J. Stat. Phys., 130:4 (2008), 801–813 | DOI | MR | Zbl
[12] U.A. Rozikov, “On q-component models on Cayley tree: contour method”, Lett. Math. Phys., 71:1 (2005), 27–38 | DOI | MR | Zbl
[13] M.M. Rahmatullaev, B.U. Abraev, “Non-translation-invariant Gibbs measures of an SOS model on a Cayley tree”, Rep. Math. Phys., 86:3 (2020), 315–324 | DOI | MR | Zbl
[14] G.I. Botirov, “Anisotropic Ising Model with Countable Set of Spin Values on Cayley Tree”, Journal of Siberian Federal University, 10:3 (2017), 305–309 | DOI | MR | Zbl
[15] M.M. Rakhmatullaev, J.D. Dehqonov, “Weakly periodic Gibbs measures for the Ising model on the Cayley tree of order $k=2$”, Theor. Math. Phys., 206:2 (2021), 184–198 | DOI | MR
[16] B.U. Abraev, “On weakly periodic ground states for the SOS model”, Scientific Bulletin of Namangan State University, 2:3 (2020), 14–21 | MR