{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/95295"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/95295","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Nonperturbative renormalization in classical φ4 theory","abstract":"This is an in-depth study of two analytic nonperturbative renormalization group methods used to study nonrelativistic quartic interacting systems. The model studied is that of classical real scalar φ4 theory. A variety of techniques are used including a rescaling of a nonlinear complete basis, a limit of finite periodic systems, and an analytic calculation of RG equations using a limit of finite systems. Assuming that the truncated forms of the action employed do not change the physics and that standard scaling techniques can be transcribed from more conventional RG approaches to these truncated forms, key results are a new fixed point at strong coupling with exponents ν=2/d and η=2 - d/2 as well as a nonperturbative generation of RG equations and subsequent solution to reduced φ4 theory. A nontrivial critical point for d=3 is identified in this reduced model with ν=4/(1+√41) ≈ 0.540 and η=0.","abstract_html":"This is an in-depth study of two analytic nonperturbative renormalization group methods used to study nonrelativistic quartic interacting systems. The model studied is that of classical real scalar φ4 theory. A variety of techniques are used including a rescaling of a nonlinear complete basis, a limit of finite periodic systems, and an analytic calculation of RG equations using a limit of finite systems. Assuming that the truncated forms of the action employed do not change the physics and that standard scaling techniques can be transcribed from more conventional RG approaches to these truncated forms, key results are a new fixed point at strong coupling with exponents ν=2/d and η=2 - d/2 as well as a nonperturbative generation of RG equations and subsequent solution to reduced φ4 theory. A nontrivial critical point for d=3 is identified in this reduced model with ν=4/(1+√41) ≈ 0.540 and η=0.","abstract_has_math":false,"creators":["Hegg, Anthony C"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":["Phillips, Philip","Ceperley, David","Leggett, Anthony","Cooper, Lance"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2017,"date_issued":"2017-03-01T15:46:14Z","date_published":"2017-03-01T15:46:14Z","updated_at":"2026-07-22T22:26:37Z","subjects":["elliptic","basis","critical point","renormalization","nonperturbative","phi-4","strong coupling","strongly coupled"],"languages":["en"],"rights":["Copyright 2016 Anthony Charles Hegg"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/95295","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Phillips, Philip","Ceperley, David","Leggett, Anthony","Cooper, Lance"]},{"key":"dc:creator","label":"Author","values":["Hegg, Anthony C"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2017-03-01T15:46:14Z","2016-10-14","2016-12"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Physics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["elliptic","basis","critical point","renormalization","nonperturbative","phi-4","strong coupling","strongly coupled"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2016 Anthony Charles Hegg"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/95295"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["This is an in-depth study of two analytic nonperturbative renormalization group methods used to study nonrelativistic quartic interacting systems. The model studied is that of classical real scalar φ4 theory. A variety of techniques are used including a rescaling of a nonlinear complete basis, a limit of finite periodic systems, and an analytic calculation of RG equations using a limit of finite systems. Assuming that the truncated forms of the action employed do not change the physics and that standard scaling techniques can be transcribed from more conventional RG approaches to these truncated forms, key results are a new fixed point at strong coupling with exponents ν=2/d and η=2 - d/2 as well as a nonperturbative generation of RG equations and subsequent solution to reduced φ4 theory. A nontrivial critical point for d=3 is identified in this reduced model with ν=4/(1+√41) ≈ 0.540 and η=0.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2017-02-28 without embargo terms","The student, Anthony Hegg, accepted the attached license on 2016-10-12 at 13:36.","The student, Anthony Hegg, submitted this Dissertation for approval on 2016-10-12 at 14:01.","This Dissertation was approved for publication on 2016-10-14 at 15:10.","DSpace SAF Submission Ingestion Package generated from Vireo submission #10188 on 2017-02-28 at 14:46:35","Made available in DSpace on 2017-03-01T15:46:14Z (GMT). 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The model studied is that of classical real scalar φ4 theory. A variety of techniques are used including a rescaling of a nonlinear complete basis, a limit of finite periodic systems, and an analytic calculation of RG equations using a limit of finite systems. Assuming that the truncated forms of the action employed do not change the physics and that standard scaling techniques can be transcribed from more conventional RG approaches to these truncated forms, key results are a new fixed point at strong coupling with exponents ν=2/d and η=2 - d/2 as well as a nonperturbative generation of RG equations and subsequent solution to reduced φ4 theory. A nontrivial critical point for d=3 is identified in this reduced model with ν=4/(1+√41) ≈ 0.540 and η=0.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2017-02-28 without embargo terms","The student, Anthony Hegg, accepted the attached license on 2016-10-12 at 13:36.","The student, Anthony Hegg, submitted this Dissertation for approval on 2016-10-12 at 14:01.","This Dissertation was approved for publication on 2016-10-14 at 15:10.","DSpace SAF Submission Ingestion Package generated from Vireo submission #10188 on 2017-02-28 at 14:46:35","Made available in DSpace on 2017-03-01T15:46:14Z (GMT). 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