Bencs, Ferenc; Boer, David de; Buys, Pjotr; Regts, Guus Uniqueness of the Gibbs measure for the anti-ferromagnetic Potts model on the infinite \(\Delta \)-regular tree for large \(\Delta \). (English) Zbl 07745916 J. Stat. Phys. 190, No. 8, Paper No. 140, 24 p. (2023). Reviewer: Utkir A. Rozikov (Tashkent) MSC: 82B20 82D40 05C05 05C63 PDFBibTeX XMLCite \textit{F. Bencs} et al., J. Stat. Phys. 190, No. 8, Paper No. 140, 24 p. (2023; Zbl 07745916) Full Text: DOI arXiv
Rahmatullaev, Muzaffar M.; Rasulova, Muhayyo A.; Asqarov, Javohir N. Ground states and Gibbs measures of Ising model with competing interactions and an external field on a Cayley tree. (English) Zbl 1515.82013 J. Stat. Phys. 190, No. 7, Paper No. 116, 15 p. (2023). MSC: 82B05 82B20 60K35 PDFBibTeX XMLCite \textit{M. M. Rahmatullaev} et al., J. Stat. Phys. 190, No. 7, Paper No. 116, 15 p. (2023; Zbl 1515.82013) Full Text: DOI arXiv
Coquille, Loren; Külske, Christof; Le Ny, Arnaud Extremal inhomogeneous Gibbs states for SOS-models and finite-spin models on trees. (English) Zbl 07672019 J. Stat. Phys. 190, No. 4, Paper No. 71, 26 p. (2023). Reviewer: Haru Pinson (Tucson) MSC: 60K35 82B20 82B26 PDFBibTeX XMLCite \textit{L. Coquille} et al., J. Stat. Phys. 190, No. 4, Paper No. 71, 26 p. (2023; Zbl 07672019) Full Text: DOI arXiv
Rozikov, U. A. Mirror symmetry of height-periodic gradient Gibbs measures of an SOS model on Cayley trees. (English) Zbl 1500.82008 J. Stat. Phys. 188, No. 3, Paper No. 26, 16 p. (2022). Reviewer: Nasir N. Ganikhodjaev (Tashkent) MSC: 82B26 82B20 60K35 05C05 PDFBibTeX XMLCite \textit{U. A. Rozikov}, J. Stat. Phys. 188, No. 3, Paper No. 26, 16 p. (2022; Zbl 1500.82008) Full Text: DOI arXiv
Mukhamedov, Farrukh; Souissi, Abdessatar Diagonalizability of quantum Markov states on trees. (English) Zbl 1473.46073 J. Stat. Phys. 182, No. 1, Paper No. 9, 15 p. (2021). Reviewer: Adam Skalski (Warszawa) MSC: 46L53 82C20 PDFBibTeX XMLCite \textit{F. Mukhamedov} and \textit{A. Souissi}, J. Stat. Phys. 182, No. 1, Paper No. 9, 15 p. (2021; Zbl 1473.46073) Full Text: DOI arXiv
Kissel, Sascha; Külske, Christof Dynamical Gibbs-non-Gibbs transitions in lattice Widom-Rowlinson models with hard-core and soft-core interactions. (English) Zbl 1434.82017 J. Stat. Phys. 178, No. 3, 725-762 (2020). MSC: 82B20 82B26 82C20 82B43 PDFBibTeX XMLCite \textit{S. Kissel} and \textit{C. Külske}, J. Stat. Phys. 178, No. 3, 725--762 (2020; Zbl 1434.82017) Full Text: DOI arXiv
Ahmad, Mohd Ali Khameini; Liao, Lingmin; Saburov, Mansoor Periodic \(p\)-adic Gibbs measures of \(q\)-state Potts model on Cayley trees. I: The chaos implies the vastness of the set of \(p\)-adic Gibbs measures. (English) Zbl 1397.82008 J. Stat. Phys. 171, No. 6, 1000-1034 (2018). Reviewer: Hasan Akin (Gaziantep) MSC: 82B20 05C05 81Q65 82B26 60K35 PDFBibTeX XMLCite \textit{M. A. K. Ahmad} et al., J. Stat. Phys. 171, No. 6, 1000--1034 (2018; Zbl 1397.82008) Full Text: DOI arXiv
Külske, Christof; Schriever, Philipp Non-robust phase transitions in the generalized clock model on trees. (English) Zbl 1394.82006 J. Stat. Phys. 170, No. 1, 1-21 (2018). Reviewer: Utkir A. Rozikov (Tashkent) MSC: 82B26 60K35 82B20 05C05 PDFBibTeX XMLCite \textit{C. Külske} and \textit{P. Schriever}, J. Stat. Phys. 170, No. 1, 1--21 (2018; Zbl 1394.82006) Full Text: DOI arXiv
Gandolfo, D.; Rahmatullaev, M. M.; Rozikov, U. A. Boundary conditions for translation-invariant Gibbs measures of the Potts model on Cayley trees. (English) Zbl 1376.82027 J. Stat. Phys. 167, No. 5, 1164-1179 (2017). MSC: 82B26 60K35 82B20 05C05 PDFBibTeX XMLCite \textit{D. Gandolfo} et al., J. Stat. Phys. 167, No. 5, 1164--1179 (2017; Zbl 1376.82027) Full Text: DOI arXiv
Cassandro, Marzio; Merola, Immacolata; Picco, Pierre Phase separation for the long range one-dimensional Ising model. (English) Zbl 1376.82016 J. Stat. Phys. 167, No. 2, 351-382 (2017). MSC: 82B20 60K35 82B43 82D40 82B26 PDFBibTeX XMLCite \textit{M. Cassandro} et al., J. Stat. Phys. 167, No. 2, 351--382 (2017; Zbl 1376.82016) Full Text: DOI arXiv
Mukhamedov, Farrukh; Barhoumi, Abdessatar; Souissi, Abdessatar Phase transitions for quantum Markov chains associated with Ising type models on a Cayley tree. (English) Zbl 1348.82034 J. Stat. Phys. 163, No. 3, 544-567 (2016). Reviewer: Artem Sapozhnikov (Leipzig) MSC: 82B26 82B20 05C05 82B44 PDFBibTeX XMLCite \textit{F. Mukhamedov} et al., J. Stat. Phys. 163, No. 3, 544--567 (2016; Zbl 1348.82034) Full Text: DOI arXiv
Kuelske, C.; Rozikov, U. A. Extremality of translation-invariant phases for a three-state SOS-model on the binary tree. (English) Zbl 1357.82023 J. Stat. Phys. 160, No. 3, 659-680 (2015). MSC: 82B26 60K35 PDFBibTeX XMLCite \textit{C. Kuelske} and \textit{U. A. Rozikov}, J. Stat. Phys. 160, No. 3, 659--680 (2015; Zbl 1357.82023) Full Text: DOI arXiv
Accardi, Luigi; Mukhamedov, Farrukh; Saburov, Mansoor On quantum Markov chains on Cayley tree. III: Ising model. (English) Zbl 1316.46046 J. Stat. Phys. 157, No. 2, 303-329 (2014). MSC: 46L53 60J99 46L60 60G50 82B20 82B26 82B27 PDFBibTeX XMLCite \textit{L. Accardi} et al., J. Stat. Phys. 157, No. 2, 303--329 (2014; Zbl 1316.46046) Full Text: DOI arXiv
Külske, C.; Rozikov, U. A.; Khakimov, R. M. Description of the translation-invariant splitting Gibbs measures for the Potts model on a Cayley tree. (English) Zbl 1298.82022 J. Stat. Phys. 156, No. 1, 189-200 (2014). MSC: 82B26 60K35 82B20 05C05 82B27 PDFBibTeX XMLCite \textit{C. Külske} et al., J. Stat. Phys. 156, No. 1, 189--200 (2014; Zbl 1298.82022) Full Text: DOI arXiv
Gandolfo, D.; Haydarov, F. H.; Rozikov, U. A.; Ruiz, J. New phase transitions of the Ising model on Cayley trees. (English) Zbl 1292.82005 J. Stat. Phys. 153, No. 3, 400-411 (2013). MSC: 82B20 82B26 PDFBibTeX XMLCite \textit{D. Gandolfo} et al., J. Stat. Phys. 153, No. 3, 400--411 (2013; Zbl 1292.82005) Full Text: DOI arXiv
Gandolfo, D.; Rakhmatullaev, M. M.; Rozikov, U. A.; Ruiz, J. On free energies of the Ising model on the Cayley tree. (English) Zbl 1273.82013 J. Stat. Phys. 150, No. 6, 1201-1217 (2013). Reviewer: Piotr Garbaczewski (Opole) MSC: 82B20 82B05 05C05 PDFBibTeX XMLCite \textit{D. Gandolfo} et al., J. Stat. Phys. 150, No. 6, 1201--1217 (2013; Zbl 1273.82013) Full Text: DOI arXiv
Alves, Rogério G.; Procacci, Aldo; Sanchis, Remy Percolation on infinite graphs and isoperimetric inequalities. (English) Zbl 1260.82041 J. Stat. Phys. 149, No. 5, 831-845 (2012). MSC: 82B43 60K35 82B20 05C40 PDFBibTeX XMLCite \textit{R. G. Alves} et al., J. Stat. Phys. 149, No. 5, 831--845 (2012; Zbl 1260.82041) Full Text: DOI arXiv
Gandolfo, Daniel; Ruiz, Jean; Shlosman, Senya A manifold of pure Gibbs states of the Ising model on a Cayley tree. (English) Zbl 1254.82008 J. Stat. Phys. 148, No. 6, 999-1005 (2012). MSC: 82B20 82B23 05C05 PDFBibTeX XMLCite \textit{D. Gandolfo} et al., J. Stat. Phys. 148, No. 6, 999--1005 (2012; Zbl 1254.82008) Full Text: DOI arXiv
Eshkabilov, Y. K.; Haydarov, F. H.; Rozikov, U. A. Non-uniqueness of Gibbs measure for models with uncountable set of spin values on a Cayley tree. (English) Zbl 1252.82026 J. Stat. Phys. 147, No. 4, 779-794 (2012). Reviewer: Nasir N. Ganikhodjaev (Kuantan) MSC: 82B20 PDFBibTeX XMLCite \textit{Y. K. Eshkabilov} et al., J. Stat. Phys. 147, No. 4, 779--794 (2012; Zbl 1252.82026) Full Text: DOI arXiv
Akin, H.; Rozikov, U. A.; Temir, S. A new set of limiting Gibbs measures for the Ising model on a Cayley tree. (English) Zbl 1211.82010 J. Stat. Phys. 142, No. 2, 314-321 (2011). Reviewer: Guy Jumarie (Montréal) MSC: 82B20 PDFBibTeX XMLCite \textit{H. Akin} et al., J. Stat. Phys. 142, No. 2, 314--321 (2011; Zbl 1211.82010) Full Text: DOI
Marchetti, D. H. U.; Sidoravicius, V.; Vares, M. E. Oriented percolation in one-dimensional \(1/|x - y|^2\) percolation models. (English) Zbl 1205.82087 J. Stat. Phys. 139, No. 6, 941-959 (2010); commentary ibid. 150, No. 4, 804-805 (2013). MSC: 82B43 82C28 PDFBibTeX XMLCite \textit{D. H. U. Marchetti} et al., J. Stat. Phys. 139, No. 6, 941--959 (2010; Zbl 1205.82087) Full Text: DOI arXiv
Ganikhodjaev, N.; Temir, S.; Akin, H. Modulated phase of a Potts model with competing binary interactions on a Cayley tree. (English) Zbl 1198.82014 J. Stat. Phys. 137, No. 4, 701-715 (2009). Reviewer: Farruh Mukhamedov (Kuantan) MSC: 82B05 82B26 PDFBibTeX XMLCite \textit{N. Ganikhodjaev} et al., J. Stat. Phys. 137, No. 4, 701--715 (2009; Zbl 1198.82014) Full Text: DOI
Rozikov, U. A. A contour method on Cayley trees. (English) Zbl 1214.82020 J. Stat. Phys. 130, No. 4, 801-813 (2008). MSC: 82B20 PDFBibTeX XMLCite \textit{U. A. Rozikov}, J. Stat. Phys. 130, No. 4, 801--813 (2008; Zbl 1214.82020) Full Text: DOI arXiv
Rozikov, U. A. A constructive description of ground states and Gibbs measures for Ising model with two-step interactions on Cayley tree. (English) Zbl 1149.82008 J. Stat. Phys. 122, No. 2, 217-235 (2006). MSC: 82B20 82B26 PDFBibTeX XMLCite \textit{U. A. Rozikov}, J. Stat. Phys. 122, No. 2, 217--235 (2006; Zbl 1149.82008) Full Text: DOI
Mukhamedov, Farruh; Rozikov, Utkir On Gibbs measures of models with competing ternary and binary interactions and corresponding von Neumann algebras. II. (English) Zbl 1071.82017 J. Stat. Phys. 119, No. 1-2, 427-446 (2005). MSC: 82B20 82B26 46L55 PDFBibTeX XMLCite \textit{F. Mukhamedov} and \textit{U. Rozikov}, J. Stat. Phys. 119, No. 1--2, 427--446 (2005; Zbl 1071.82017) Full Text: DOI arXiv