{"id":"https://openalex.org/W2063597527","doi":"https://doi.org/10.1103/physrevb.5.383","title":"Pair Effects in Substitutional Alloys. I. Systematic Analysis of the Coherent-Potential Approximation","display_name":"Pair Effects in Substitutional Alloys. I. Systematic Analysis of the Coherent-Potential Approximation","publication_year":1972,"publication_date":"1972-01-15","ids":{"openalex":"https://openalex.org/W2063597527","doi":"https://doi.org/10.1103/physrevb.5.383","mag":"2063597527"},"language":"en","primary_location":{"id":"doi:10.1103/physrevb.5.383","doi":"https://doi.org/10.1103/physrevb.5.383","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physrevb.5.383","pdf_url":null,"source":{"id":"https://openalex.org/S4210208989","display_name":"Physical review. B, Solid state","issn_l":"0556-2805","issn":["0556-2805"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review B","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5108074959","display_name":"Lawrence Schwartz","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"L. Schwartz","raw_affiliation_strings":["Division of Engineering and Applied Physics, Harvard University, Cambridge, Massachusetts 02138"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Division of Engineering and Applied Physics, Harvard University, Cambridge, Massachusetts 02138","institution_ids":["https://openalex.org/I136199984"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036408112","display_name":"Eric D. Siggia","orcid":"https://orcid.org/0000-0001-7482-1854","observed_orcids":["https://orcid.org/0000-0001-7482-1854"]},"institutions":[{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"E. Siggia","raw_affiliation_strings":["Division of Engineering and Applied Physics, Harvard University, Cambridge, Massachusetts 02138"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Division of Engineering and Applied Physics, Harvard University, Cambridge, Massachusetts 02138","institution_ids":["https://openalex.org/I136199984"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I136199984"],"apc_list":null,"apc_paid":null,"fwci":62.1483,"has_fulltext":false,"cited_by_count":110,"citation_normalized_percentile":{"value":0.99959826,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":96},"biblio":{"volume":"5","issue":"2","first_page":"383","last_page":"396"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13645","display_name":"Thermodynamic and Structural Properties of Metals and Alloys","score":0.9922000169754028,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13645","display_name":"Thermodynamic and Structural Properties of Metals and Alloys","score":0.9922000169754028,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10591","display_name":"Theoretical and Computational Physics","score":0.002099999925121665,"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/T10037","display_name":"Physics of Superconductivity and Magnetism","score":0.0012000000569969416,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/coherent-potential-approximation","display_name":"coherent potential approximation","score":0.9629999995231628},{"id":"https://openalex.org/keywords/substitutional-alloys","display_name":"substitutional alloys","score":0.8209999799728394},{"id":"https://openalex.org/keywords/disordered-binary-alloys","display_name":"disordered binary alloys","score":0.8429999947547913},{"id":"https://openalex.org/keywords/electron-self-energy","display_name":"electron self-energy","score":0.7990000247955322},{"id":"https://openalex.org/keywords/short-range-order","display_name":"short-range order","score":0.8519999980926514},{"id":"https://openalex.org/keywords/chemical-disorder","display_name":"chemical disorder","score":0.8169999718666077},{"id":"https://openalex.org/keywords/density-of-states","display_name":"density of states","score":0.921999990940094},{"id":"https://openalex.org/keywords/single-band-model","display_name":"one-band model","score":0.6620000004768372}],"concepts":[{"id":"https://openalex.org/C2780732345","wikidata":"https://www.wikidata.org/wiki/Q5141360","display_name":"Coherent potential approximation","level":3,"score":0.8123027682304382},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.7191482782363892},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.7124234437942505},{"id":"https://openalex.org/C71987851","wikidata":"https://www.wikidata.org/wiki/Q7216430","display_name":"Impurity","level":2,"score":0.5407675504684448},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5129880309104919},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.47028329968452454},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.4616836905479431},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.4174080789089203},{"id":"https://openalex.org/C86025842","wikidata":"https://www.wikidata.org/wiki/Q5358432","display_name":"Electronic structure","level":2,"score":0.3581875264644623},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.09738081693649292},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C558565934","wikidata":"https://www.wikidata.org/wiki/Q2743","display_name":"Musical","level":2,"score":0.0},{"id":"https://openalex.org/C153349607","wikidata":"https://www.wikidata.org/wiki/Q36649","display_name":"Visual arts","level":1,"score":0.0},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1103/physrevb.5.383","doi":"https://doi.org/10.1103/physrevb.5.383","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physrevb.5.383","pdf_url":null,"source":{"id":"https://openalex.org/S4210208989","display_name":"Physical review. B, Solid state","issn_l":"0556-2805","issn":["0556-2805"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review B","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1965027006","https://openalex.org/W1990804328","https://openalex.org/W1999532499","https://openalex.org/W2007480407","https://openalex.org/W2012390195","https://openalex.org/W2018733645","https://openalex.org/W2028912160","https://openalex.org/W2046413705","https://openalex.org/W2055022593","https://openalex.org/W2057628482","https://openalex.org/W2060192542","https://openalex.org/W2064234754","https://openalex.org/W2066364117","https://openalex.org/W2078770790","https://openalex.org/W2090098293","https://openalex.org/W2092274425","https://openalex.org/W2103230617","https://openalex.org/W2123081481","https://openalex.org/W4296239410"],"related_works":["https://openalex.org/W1989008065","https://openalex.org/W2064640045","https://openalex.org/W6987626870","https://openalex.org/W2092274425","https://openalex.org/W2055044386","https://openalex.org/W1978972642","https://openalex.org/W2070707571","https://openalex.org/W16424736","https://openalex.org/W1975503880","https://openalex.org/W2051515581"],"abstract_inverted_index":{"A":[0,159],"single-band":[1,179],"model":[2],"is":[3,27,46,50,161,181,204,207],"used":[4,17],"to":[5,18,58,61,99,102,106,115,133,145,163,183,209],"study":[6],"the":[7,23,37,42,51,65,72,76,103,127,147,156,165,168,178,185,191,200,211],"electronic":[8],"structure":[9],"of":[10,29,53,82,92,111,126,149,155,171,187,195,202],"disordered":[11],"binary":[12],"alloys.":[13],"Functional-derivative":[14],"techniques":[15],"are":[16,90,113,141],"generate":[19],"an":[20],"expansion":[21],"for":[22,41],"electron":[24],"self-energy":[25],"that":[26,36,89,122],"free":[28],"all":[30,110],"\"multiple-occupancy\"":[31],"corrections.":[32],"This":[33],"analysis":[34],"reveals":[35],"relevant":[38],"small":[39],"parameter":[40],"coherent-potential":[43],"approximation":[44],"(CPA)":[45],"${Z}^{\\ensuremath{-}1}$,":[47],"where":[48],"$Z$":[49],"number":[52],"nearest":[54],"neighbors.":[55],"In":[56],"addition":[57],"being":[59],"exact":[60,114],"first":[62],"order":[63,70,84,116,176,189,198],"in":[64,71,85,136,190],"concentration":[66],"$x$":[67,86],"and":[68,87,118,143,206],"third":[69],"impurity":[73,157],"potential":[74],"$\\ensuremath{\\delta}$,":[75],"CPA":[77,104,128],"retains":[78],"just":[79],"those":[80],"contributions":[81],"higher":[83,134],"$\\ensuremath{\\delta}$":[88],"independent":[91],"${Z}^{\\ensuremath{-}1}$.":[93,137],"Various":[94],"methods":[95],"have":[96],"been":[97],"suggested":[98],"calculate":[100],"corrections":[101],"due":[105],"two-atom":[107],"clusters.":[108],"While":[109],"these":[112],"${x}^{2}$":[117],"${\\ensuremath{\\delta}}^{5}$,":[119],"we":[120],"argue":[121],"a":[123],"proper":[124],"generalization":[125],"must":[129],"also":[130],"be":[131],"correct":[132],"orders":[135],"The":[138,193],"appropriate":[139],"equations":[140],"derived":[142],"shown":[144,208],"imply":[146,184],"existence":[148,186],"satellite":[150],"levels":[151],"on":[152,199],"either":[153],"side":[154],"subband.":[158],"formalism":[160],"developed":[162],"examine":[164],"departure":[166],"from":[167],"usual":[169],"assumption":[170],"complete":[172],"compositional":[173],"disorder.":[174],"To":[175],"${x}^{2}$,":[177],"Hamiltonian":[180],"found":[182],"short-range":[188,197],"alloy.":[192],"influence":[194],"this":[196],"density":[201],"states":[203],"discussed":[205],"modify":[210],"clustering":[212],"effects":[213],"previously":[214],"evaluated.":[215]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}
