{"id":"https://openalex.org/W2999816623","doi":"https://doi.org/10.37236/320","title":"Aperiodic Non-Isomorphic Lattices with Equivalent Percolation and Random-Cluster Models","display_name":"Aperiodic Non-Isomorphic Lattices with Equivalent Percolation and Random-Cluster Models","publication_year":2010,"publication_date":"2010-03-29","ids":{"openalex":"https://openalex.org/W2999816623","doi":"https://doi.org/10.37236/320","mag":"2999816623"},"language":"en","primary_location":{"id":"doi:10.37236/320","is_oa":true,"landing_page_url":"https://doi.org/10.37236/320","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1r48/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1r48/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035765654","display_name":"Klas Markstr\u00f6m","orcid":"https://orcid.org/0000-0002-6344-1642"},"institutions":[{"id":"https://openalex.org/I90267481","display_name":"Ume\u00e5 University","ror":"https://ror.org/05kb8h459","country_code":"SE","type":"education","lineage":["https://openalex.org/I90267481"]},{"id":"https://openalex.org/I1279596006","display_name":"Statistics Sweden","ror":"https://ror.org/05x7wz523","country_code":"SE","type":"government","lineage":["https://openalex.org/I1279596006"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"Klas Markstr\u00f6m","raw_affiliation_strings":["Department of Mathematics and Mathematical Statistics, Ume\u00e5 University, Sweden"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Mathematical Statistics, Ume\u00e5 University, Sweden","institution_ids":["https://openalex.org/I1279596006","https://openalex.org/I90267481"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064543263","display_name":"John C. Wierman","orcid":"https://orcid.org/0000-0002-5000-9455"},"institutions":[{"id":"https://openalex.org/I145311948","display_name":"Johns Hopkins University","ror":"https://ror.org/00za53h95","country_code":"US","type":"education","lineage":["https://openalex.org/I145311948"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"John C. Wierman","raw_affiliation_strings":["Department of Applied Mathematics and Statistics, Johns Hopkins University, USA"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Statistics, Johns Hopkins University, USA","institution_ids":["https://openalex.org/I145311948"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5035765654"],"corresponding_institution_ids":["https://openalex.org/I1279596006","https://openalex.org/I90267481"],"apc_list":null,"apc_paid":null,"fwci":0.4032,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.6332264,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"17","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9994999766349792,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9994999766349792,"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/T10591","display_name":"Theoretical and Computational Physics","score":0.9958000183105469,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/mathematics","display_name":"Mathematics","score":0.8214178085327148},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6474255919456482},{"id":"https://openalex.org/keywords/continuum-percolation-theory","display_name":"Continuum percolation theory","score":0.5538559556007385},{"id":"https://openalex.org/keywords/percolation-critical-exponents","display_name":"Percolation critical exponents","score":0.5526005625724792},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5254232883453369},{"id":"https://openalex.org/keywords/percolation-threshold","display_name":"Percolation threshold","score":0.5176820755004883},{"id":"https://openalex.org/keywords/aperiodic-graph","display_name":"Aperiodic graph","score":0.41070157289505005},{"id":"https://openalex.org/keywords/critical-exponent","display_name":"Critical exponent","score":0.179133802652359},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1350472867488861},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.0892937183380127}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8214178085327148},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6474255919456482},{"id":"https://openalex.org/C177634923","wikidata":"https://www.wikidata.org/wiki/Q17005777","display_name":"Continuum percolation theory","level":5,"score":0.5538559556007385},{"id":"https://openalex.org/C158574103","wikidata":"https://www.wikidata.org/wiki/Q7167168","display_name":"Percolation critical exponents","level":4,"score":0.5526005625724792},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5254232883453369},{"id":"https://openalex.org/C2729557","wikidata":"https://www.wikidata.org/wiki/Q7167170","display_name":"Percolation threshold","level":3,"score":0.5176820755004883},{"id":"https://openalex.org/C104247578","wikidata":"https://www.wikidata.org/wiki/Q4779368","display_name":"Aperiodic graph","level":2,"score":0.41070157289505005},{"id":"https://openalex.org/C164154869","wikidata":"https://www.wikidata.org/wiki/Q901927","display_name":"Critical exponent","level":3,"score":0.179133802652359},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1350472867488861},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.0892937183380127},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C69990965","wikidata":"https://www.wikidata.org/wiki/Q65402698","display_name":"Electrical resistivity and conductivity","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/320","is_oa":true,"landing_page_url":"https://doi.org/10.37236/320","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1r48/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/320","is_oa":true,"landing_page_url":"https://doi.org/10.37236/320","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1r48/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320310145","display_name":"Johns Hopkins University","ror":"https://ror.org/00za53h95"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2999816623.pdf","grobid_xml":"https://content.openalex.org/works/W2999816623.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W186284027","https://openalex.org/W1519008042","https://openalex.org/W1529174649","https://openalex.org/W1590167836","https://openalex.org/W1594827281","https://openalex.org/W1597152871","https://openalex.org/W1626881312","https://openalex.org/W1982314856","https://openalex.org/W1996399134","https://openalex.org/W2057563319","https://openalex.org/W2058283287","https://openalex.org/W2070263216","https://openalex.org/W2073765477","https://openalex.org/W2112961480","https://openalex.org/W2159018842","https://openalex.org/W2165422922","https://openalex.org/W2166935116","https://openalex.org/W2295578127","https://openalex.org/W2949752565","https://openalex.org/W3037140745","https://openalex.org/W3102784541","https://openalex.org/W4302344174","https://openalex.org/W4388438965"],"related_works":["https://openalex.org/W2949162805","https://openalex.org/W3106053424","https://openalex.org/W4226254281","https://openalex.org/W2944372371","https://openalex.org/W2014145684","https://openalex.org/W3108633931","https://openalex.org/W1983827001","https://openalex.org/W2077569955","https://openalex.org/W2082819662","https://openalex.org/W2080696508"],"abstract_inverted_index":{"We":[0],"explicitly":[1,15,99],"construct":[2],"an":[3],"uncountable":[4],"class":[5],"of":[6,37,45,56,73,84,104],"infinite":[7],"aperiodic":[8],"plane":[9,89],"graphs":[10,47,66],"which":[11],"have":[12],"equal,":[13],"and":[14,25,41,58],"computable,":[16],"bond":[17,23,94,120],"percolation":[18,24,39,95,121],"thresholds.":[19],"Furthermore":[20],"for":[21,53,61],"both":[22],"the":[26,35,38,42,46,62,102,118],"random-cluster":[27,63],"model":[28],"all":[29,54,59],"large":[30],"scale":[31],"properties,":[32],"such":[33],"as":[34,101],"values":[36,55],"threshold":[40,96,122],"critical":[43],"exponents,":[44],"are":[48,67],"equal.":[49],"This":[50],"equivalence":[51],"holds":[52],"$p$":[57],"$q\\in[0,\\infty]$":[60],"model.":[64],"The":[65,92],"constructed":[68],"by":[69,107],"placing":[70],"a":[71,74,85,105,109],"copy":[72],"rotor":[75],"gadget":[76],"graph":[77],"or":[78],"its":[79],"reflection":[80],"in":[81],"each":[82],"hyperedge":[83],"connected":[86],"self-dual":[87],"3-uniform":[88],"hypergraph":[90],"lattice.":[91],"exact":[93],"may":[97],"be":[98],"determined":[100],"root":[103],"polynomial":[106],"using":[108],"generalised":[110],"star-triangle":[111],"transformation.":[112],"Related":[113],"randomly":[114],"oriented":[115],"models":[116],"share":[117],"same":[119],"value.":[123]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}