{"id":"https://openalex.org/W4281761893","doi":"https://doi.org/10.4213/tmf10245","title":"\u041c\u0435\u0440\u044b \u0413\u0438\u0431\u0431\u0441\u0430 \u0434\u043b\u044f \u043c\u043e\u0434\u0435\u043b\u0438 HC-\u0411\u043b\u044e\u043c\u0430-\u041a\u0430\u043f\u0435\u043b\u044f \u0441\u043e \u0441\u0447\u0435\u0442\u043d\u044b\u043c \u0447\u0438\u0441\u043b\u043e\u043c \u0441\u043e\u0441\u0442\u043e\u044f\u043d\u0438\u0439 \u043d\u0430 \u0434\u0435\u0440\u0435\u0432\u0435 \u041a\u044d\u043b\u0438","display_name":"\u041c\u0435\u0440\u044b \u0413\u0438\u0431\u0431\u0441\u0430 \u0434\u043b\u044f \u043c\u043e\u0434\u0435\u043b\u0438 HC-\u0411\u043b\u044e\u043c\u0430-\u041a\u0430\u043f\u0435\u043b\u044f \u0441\u043e \u0441\u0447\u0435\u0442\u043d\u044b\u043c \u0447\u0438\u0441\u043b\u043e\u043c \u0441\u043e\u0441\u0442\u043e\u044f\u043d\u0438\u0439 \u043d\u0430 \u0434\u0435\u0440\u0435\u0432\u0435 \u041a\u044d\u043b\u0438","publication_year":2022,"publication_date":"2022-05-29","ids":{"openalex":"https://openalex.org/W4281761893","doi":"https://doi.org/10.4213/tmf10245"},"language":"ru","primary_location":{"id":"doi:10.4213/tmf10245","doi":"https://doi.org/10.4213/tmf10245","is_oa":true,"landing_page_url":"https://doi.org/10.4213/tmf10245","pdf_url":"http://www.mathnet.ru/php/getRefFromDB.phtml?jrnid=tmf&paperid=10245&output=pdf&option_lang=rus","source":{"id":"https://openalex.org/S4210179734","display_name":"\u0422\u0435\u043e\u0440\u0435\u0442\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0438 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0444\u0438\u0437\u0438\u043a\u0430","issn_l":"0564-6162","issn":["0564-6162","2305-3135"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["russia-white-list-1"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"\u0422\u0435\u043e\u0440\u0435\u0442\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0438 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0444\u0438\u0437\u0438\u043a\u0430","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"http://www.mathnet.ru/php/getRefFromDB.phtml?jrnid=tmf&paperid=10245&output=pdf&option_lang=rus","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038626030","display_name":"\u041d\u0430\u0441\u0438\u0440 \u041d\u0430\u0431\u0438\u0435\u0432\u0438\u0447 \u0413\u0430\u043d\u0438\u0445\u043e\u0434\u0436\u0430\u0435\u0432","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I1302269238","display_name":"Academy of Sciences Republic of Uzbekistan","ror":"https://ror.org/01xgfaw76","country_code":"UZ","type":"government","lineage":["https://openalex.org/I1302269238","https://openalex.org/I4405266844"]}],"countries":["UZ"],"is_corresponding":false,"raw_author_name":"Nasir Nabievich Ganikhodzhaev","raw_affiliation_strings":["Romanovskii Institute for Mathematics, UzAS, Tashkent, Uzbekistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Romanovskii Institute for Mathematics, UzAS, Tashkent, Uzbekistan","institution_ids":["https://openalex.org/I1302269238"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027981226","display_name":"Utkir Abdulloevich Rozikov","orcid":"https://orcid.org/0000-0001-9795-2566","observed_orcids":["https://orcid.org/0000-0001-9795-2566"]},"institutions":[{"id":"https://openalex.org/I1302269238","display_name":"Academy of Sciences Republic of Uzbekistan","ror":"https://ror.org/01xgfaw76","country_code":"UZ","type":"government","lineage":["https://openalex.org/I1302269238","https://openalex.org/I4405266844"]},{"id":"https://openalex.org/I4210096951","display_name":"Central Asian University","ror":"https://ror.org/00x6wnm78","country_code":"UZ","type":"education","lineage":["https://openalex.org/I4210096951"]},{"id":"https://openalex.org/I47151758","display_name":"National University of Uzbekistan","ror":"https://ror.org/011647w73","country_code":"UZ","type":"education","lineage":["https://openalex.org/I47151758"]}],"countries":["UZ"],"is_corresponding":false,"raw_author_name":"Utkir Abdulloevich Rozikov","raw_affiliation_strings":["AKFA University, Tashkent, Uzbekistan","Romanovskii Institute for Mathematics, UzAS, Tashkent, Uzbekistan","Ulugbek National University of Uzbekistan, Tashkent, Uzbekistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"AKFA University, Tashkent, Uzbekistan","institution_ids":["https://openalex.org/I4210096951"]},{"raw_affiliation_string":"Romanovskii Institute for Mathematics, UzAS, Tashkent, Uzbekistan","institution_ids":["https://openalex.org/I1302269238"]},{"raw_affiliation_string":"Ulugbek National University of Uzbekistan, Tashkent, Uzbekistan","institution_ids":["https://openalex.org/I47151758"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009438826","display_name":"Nosirzhon Muidinovich Khatamov","orcid":"https://orcid.org/0000-0002-2902-7982","observed_orcids":["https://orcid.org/0000-0002-2902-7982"]},"institutions":[{"id":"https://openalex.org/I1302269238","display_name":"Academy of Sciences Republic of Uzbekistan","ror":"https://ror.org/01xgfaw76","country_code":"UZ","type":"government","lineage":["https://openalex.org/I1302269238","https://openalex.org/I4405266844"]},{"id":"https://openalex.org/I160547875","display_name":"Namangan State University","ror":"https://ror.org/00k8k8t47","country_code":"UZ","type":"education","lineage":["https://openalex.org/I160547875"]}],"countries":["UZ"],"is_corresponding":false,"raw_author_name":"Nosirzhon Muidinovich Khatamov","raw_affiliation_strings":["Namangan State University, Namangan, Uzbekistan","Romanovskii Institute for Mathematics, UzAS, Tashkent, Uzbekistan"],"raw_orcid":"https://orcid.org/0000-0002-2902-7982","affiliations":[{"raw_affiliation_string":"Namangan State University, Namangan, Uzbekistan","institution_ids":["https://openalex.org/I160547875"]},{"raw_affiliation_string":"Romanovskii Institute for Mathematics, UzAS, Tashkent, Uzbekistan","institution_ids":["https://openalex.org/I1302269238"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2534,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.30891331,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":93},"biblio":{"volume":"211","issue":"3","first_page":"491","last_page":"501"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13234","display_name":"p-Adic Analysis and Mathematical Physics","score":0.40549999475479126,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13234","display_name":"p-Adic Analysis and Mathematical Physics","score":0.40549999475479126,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.38179999589920044,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.13819999992847443,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/gibbs-measures","display_name":"Gibbs measures","score":0.8939999938011169},{"id":"https://openalex.org/keywords/cayley-tree","display_name":"Cayley tree","score":0.7250000238418579},{"id":"https://openalex.org/keywords/nearest-neighbor-interactions","display_name":"nearest-neighbor interactions","score":0.625},{"id":"https://openalex.org/keywords/translation-invariant-gibbs-measures","display_name":"translation-invariant Gibbs measures","score":0.7979999780654907},{"id":"https://openalex.org/keywords/uniqueness-of-gibbs-measures","display_name":"uniqueness of Gibbs measures","score":0.9459999799728394},{"id":"https://openalex.org/keywords/critical-threshold","display_name":"critical threshold","score":0.4699999988079071}],"concepts":[{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.621250569820404},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5078862309455872},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.27440017461776733}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.4213/tmf10245","doi":"https://doi.org/10.4213/tmf10245","is_oa":true,"landing_page_url":"https://doi.org/10.4213/tmf10245","pdf_url":"http://www.mathnet.ru/php/getRefFromDB.phtml?jrnid=tmf&paperid=10245&output=pdf&option_lang=rus","source":{"id":"https://openalex.org/S4210179734","display_name":"\u0422\u0435\u043e\u0440\u0435\u0442\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0438 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0444\u0438\u0437\u0438\u043a\u0430","issn_l":"0564-6162","issn":["0564-6162","2305-3135"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["russia-white-list-1"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"\u0422\u0435\u043e\u0440\u0435\u0442\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0438 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0444\u0438\u0437\u0438\u043a\u0430","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.4213/tmf10245","doi":"https://doi.org/10.4213/tmf10245","is_oa":true,"landing_page_url":"https://doi.org/10.4213/tmf10245","pdf_url":"http://www.mathnet.ru/php/getRefFromDB.phtml?jrnid=tmf&paperid=10245&output=pdf&option_lang=rus","source":{"id":"https://openalex.org/S4210179734","display_name":"\u0422\u0435\u043e\u0440\u0435\u0442\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0438 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0444\u0438\u0437\u0438\u043a\u0430","issn_l":"0564-6162","issn":["0564-6162","2305-3135"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["russia-white-list-1"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"\u0422\u0435\u043e\u0440\u0435\u0442\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0438 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0444\u0438\u0437\u0438\u043a\u0430","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4281761893.pdf","grobid_xml":"https://content.openalex.org/works/W4281761893.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W584162502","https://openalex.org/W1645243942","https://openalex.org/W1979666361","https://openalex.org/W2006535639","https://openalex.org/W2056262613","https://openalex.org/W2074100739","https://openalex.org/W2077090160","https://openalex.org/W2163208395","https://openalex.org/W2318866578","https://openalex.org/W2810051596","https://openalex.org/W2912892106","https://openalex.org/W2963972580","https://openalex.org/W2971798843","https://openalex.org/W3007524713","https://openalex.org/W3038341369","https://openalex.org/W3080272619","https://openalex.org/W3093661711","https://openalex.org/W3133075102","https://openalex.org/W3133841062","https://openalex.org/W3139154464","https://openalex.org/W3146725539","https://openalex.org/W3173348074","https://openalex.org/W3211629563","https://openalex.org/W4238583669","https://openalex.org/W4248019092","https://openalex.org/W4255308044"],"related_works":["https://openalex.org/W7220974601","https://openalex.org/W4293403709","https://openalex.org/W4391407531","https://openalex.org/W4225812598","https://openalex.org/W4283375845","https://openalex.org/W3038341369","https://openalex.org/W6893290092","https://openalex.org/W7166549684","https://openalex.org/W4408926798","https://openalex.org/W2550386137"],"abstract_inverted_index":{"\u0418\u0437\u0443\u0447\u0430\u0435\u0442\u0441\u044f":[0],"\u043c\u043e\u0434\u0435\u043b\u044c":[1],"HC-\u0411\u043b\u044e\u043c\u0430-\u041a\u0430\u043f\u0435\u043b\u044f":[2],"\u0441\u043e":[3],"\u0441\u0447\u0435\u0442\u043d\u044b\u043c":[4],"\u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u043e\u043c":[5],"$\\mathbb":[6],"Z$":[7],"\u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439":[8],"\u0441\u043f\u0438\u043d\u0430":[9],"\u0438":[10,55],"\u0441\u0438\u043b\u043e\u0439":[11],"\u0432\u0437\u0430\u0438\u043c\u043e\u0434\u0435\u0439\u0441\u0442\u0432\u0438\u044f":[12],"$J\\in":[13],"\\mathbb":[14],"R$":[15],"\u0431\u043b\u0438\u0436\u0430\u0439\u0448\u0438\u0445":[16],"\u0441\u043e\u0441\u0435\u0434\u0435\u0439":[17],"\u043d\u0430":[18],"\u0434\u0435\u0440\u0435\u0432\u0435":[19],"\u041a\u044d\u043b\u0438":[20],"\u043f\u043e\u0440\u044f\u0434\u043a\u0430":[21],"$k\\geq":[22],"2$.":[23],"\u041f\u043e\u043b\u0443\u0447\u0435\u043d\u044b":[24],"\u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435":[25],"\u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u044b.":[26],"\u041f\u0443\u0441\u0442\u044c":[27,53],"$\\theta=e^{-J/T}$,":[28],"$T>0$":[29],"-":[30],"\u0442\u0435\u043c\u043f\u0435\u0440\u0430\u0442\u0443\u0440\u0430.":[31],"\u041f\u0440\u0438":[32,46,70],"$\\theta\\geq1$":[33],"\u043d\u0435":[34,41],"\u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u044e\u0442":[35,42,72],"\u0442\u0440\u0430\u043d\u0441\u043b\u044f\u0446\u0438\u043e\u043d\u043d\u043e-\u0438\u043d\u0432\u0430\u0440\u0438\u0430\u043d\u0442\u043d\u044b\u0435":[36],"\u043c\u0435\u0440\u044b":[37,44,51,76],"\u0413\u0438\u0431\u0431\u0441\u0430,":[38,64,77],"\u0430":[39],"\u0442\u0430\u043a\u0436\u0435":[40],"2-\u043f\u0435\u0440\u0438\u043e\u0434\u0438\u0447\u0435\u0441\u043a\u0438\u0435":[43,75],"\u0413\u0438\u0431\u0431\u0441\u0430.":[45,52,69,84],"$0<\\theta<1$":[47],"\u0434\u043e\u043a\u0430\u0437\u0430\u043d\u0430":[48],"\u0435\u0434\u0438\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u043e\u0441\u0442\u044c":[49],"\u0442\u0440\u0430\u043d\u0441\u043b\u044f\u0446\u0438\u043e\u043d\u043d\u043e-\u0438\u043d\u0432\u0430\u0440\u0438\u0430\u043d\u0442\u043d\u043e\u0439":[50,67,82],"$\\Theta=\\sum_i\\theta^{(k+1)i^2}$":[54],"$\\Theta_\\mathrm{cr}(k)=k^k/(k-1)^{k+1}$.":[56],"\u0415\u0441\u043b\u0438":[57],"$0<\\Theta\\leq\\Theta_\\mathrm{cr}$,":[58],"\u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442":[59],"\u0440\u043e\u0432\u043d\u043e":[60,73],"\u043e\u0434\u043d\u0430":[61,78],"2-\u043f\u0435\u0440\u0438\u043e\u0434\u0438\u0447\u0435\u0441\u043a\u0430\u044f":[62],"\u043c\u0435\u0440\u0430":[63],"\u043a\u043e\u0442\u043e\u0440\u0430\u044f":[65],"\u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f":[66,81],"\u043c\u0435\u0440\u043e\u0439":[68,83],"$\\Theta>\\Theta_\\mathrm{cr}$":[71],"\u0442\u0440\u0438":[74],"\u0438\u0437":[79],"\u043a\u043e\u0442\u043e\u0440\u044b\u0445":[80]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2022-06-13T00:00:00"}
