{"id":{"repo_id":"aachen","oai_identifier":"oai:publications.rwth-aachen.de:50011"},"canonical_url":"https://search.dev.ndltd.org/etd/aachen/oai:publications.rwth-aachen.de:50011","repository":{"repo_id":"aachen","name":"RWTH Aachen University","base_url":"https://publications.rwth-aachen.de/oai2d"},"display":{"title":"Optimierte Borelsummation von kritischen Exponenten und universellen Amplitudenverhältnissen im phi 4-Modell","abstract":"Second order phase transitions are investigated with theoretical methods of the phi^4 field theory. Thermodynamic quantities like the correlation length, the susceptibility or the specific heat have singularities in the critical point. The goal is the precise temperature dependence near these singularities. A cooperative many particel effect generates critical behavior. Differences in the short range microscopic interaction of the investigated systems are insignificant. The dimension d and the number of components of the order parameter determine the critical behavior. The renormalization group theory identifies universality classes of critical behavior and predicts that critical exponents and certain amplitude ratios are equal for all systems of the same universality class. The case d=3, n=2 is of special interest. Experimental results of the superfluid transition of 4^He in space are compared to MC simulations of spin systems and analytical calculations in the framework of the phi^4 theory. This is a high precision test of the RG prediction of universality. RG theory has a wide range of applications. Hence, this quantitative test of RG is of interest in statistical physics, condensed matter physics and elementary particle physics. A short summary of two main results: A significant improvement of former Borel summations of critical exponents gamma and alpha is achieved with the same information of perturbation series. This improvement stems from an enhancement of the method of resummation. Amplitude functions at the fixpoint are resummed. Analytical results for certain universal amplitude ratios are achieved. So far only numerical or experimental quantitative results for these ratios are known.","abstract_html":"Second order phase transitions are investigated with theoretical methods of the phi^4 field theory. Thermodynamic quantities like the correlation length, the susceptibility or the specific heat have singularities in the critical point. The goal is the precise temperature dependence near these singularities. A cooperative many particel effect generates critical behavior. Differences in the short range microscopic interaction of the investigated systems are insignificant. The dimension d and the number of components of the order parameter determine the critical behavior. The renormalization group theory identifies universality classes of critical behavior and predicts that critical exponents and certain amplitude ratios are equal for all systems of the same universality class. The case d=3, n=2 is of special interest. Experimental results of the superfluid transition of 4^He in space are compared to MC simulations of spin systems and analytical calculations in the framework of the phi^4 theory. This is a high precision test of the RG prediction of universality. RG theory has a wide range of applications. Hence, this quantitative test of RG is of interest in statistical physics, condensed matter physics and elementary particle physics. A short summary of two main results: A significant improvement of former Borel summations of critical exponents gamma and alpha is achieved with the same information of perturbation series. This improvement stems from an enhancement of the method of resummation. Amplitude functions at the fixpoint are resummed. Analytical results for certain universal amplitude ratios are achieved. So far only numerical or experimental quantitative results for these ratios are known.","abstract_has_math":false,"creators":["Cremer, Daniel"],"institution":"Publikationsserver der RWTH Aachen University","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Dohm, Volker"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2008,"date_issued":"2008","date_published":"2008","updated_at":"2026-07-30T19:40:16Z","subjects":["info:eu-repo/classification/ddc/530","Physik","Phasenübergänge","kritische Exponenten","universelle Amplitudenverhältnisse","phase transitions","critical exponents","universal amplitude ratios"],"languages":["ger"],"rights":["info:eu-repo/semantics/openAccess"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-112576%22"],"render_values":[{"text":"https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-112576%22","href":"https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-112576%22","code":true}]}]},"links":{"outbound_url":"https://publications.rwth-aachen.de/record/50011","outbound_label":"Repository record","outbound_source":"dc:identifier"},"source_record":{"url":"https://publications.rwth-aachen.de/oai2d?verb=GetRecord&metadataPrefix=oai_dc&identifier=oai%3Apublications.rwth-aachen.de%3A50011","prefix":"oai_dc"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Dohm, Volker"]},{"key":"dc:creator","label":"Author","values":["Cremer, Daniel"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:coverage","label":"Dc Coverage","values":["DE"]},{"key":"dc:date","label":"Dc Date","values":["2008"]},{"key":"dc:publisher","label":"Institution","values":["Publikationsserver der RWTH Aachen University"]},{"key":"dc:relation","label":"Dc Relation","values":["info:eu-repo/semantics/altIdentifier/urn/urn:nbn:de:hbz:82-opus-22522"]},{"key":"dc:type","label":"Dc Type","values":["info:eu-repo/semantics/doctoralThesis","info:eu-repo/semantics/publishedVersion"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["info:eu-repo/classification/ddc/530","Physik","Phasenübergänge","kritische Exponenten","universelle Amplitudenverhältnisse","phase transitions","critical exponents","universal amplitude ratios"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["ger"]},{"key":"dc:rights","label":"Dc Rights","values":["info:eu-repo/semantics/openAccess"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://publications.rwth-aachen.de/record/50011","https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-112576%22"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Second order phase transitions are investigated with theoretical methods of the phi^4 field theory. Thermodynamic quantities like the correlation length, the susceptibility or the specific heat have singularities in the critical point. The goal is the precise temperature dependence near these singularities. A cooperative many particel effect generates critical behavior. Differences in the short range microscopic interaction of the investigated systems are insignificant. The dimension d and the number of components of the order parameter determine the critical behavior. The renormalization group theory identifies universality classes of critical behavior and predicts that critical exponents and certain amplitude ratios are equal for all systems of the same universality class. The case d=3, n=2 is of special interest. Experimental results of the superfluid transition of 4^He in space are compared to MC simulations of spin systems and analytical calculations in the framework of the phi^4 theory. This is a high precision test of the RG prediction of universality. RG theory has a wide range of applications. Hence, this quantitative test of RG is of interest in statistical physics, condensed matter physics and elementary particle physics. A short summary of two main results: A significant improvement of former Borel summations of critical exponents gamma and alpha is achieved with the same information of perturbation series. This improvement stems from an enhancement of the method of resummation. Amplitude functions at the fixpoint are resummed. Analytical results for certain universal amplitude ratios are achieved. So far only numerical or experimental quantitative results for these ratios are known."]},{"key":"dc:source","label":"Dc Source","values":["Aachen : Publikationsserver der RWTH Aachen University 151 S. : graph. Darst. (2008). = Aachen, Techn. Hochsch., Diss., 2008"]},{"key":"dc:title","label":"Title","values":["Optimierte Borelsummation von kritischen Exponenten und universellen Amplitudenverhältnissen im phi 4-Modell"]}]}],"canonical_facts":{"dc:contributor":["Dohm, Volker"],"dc:coverage":["DE"],"dc:creator":["Cremer, Daniel"],"dc:date":["2008"],"dc:description":["Second order phase transitions are investigated with theoretical methods of the phi^4 field theory. Thermodynamic quantities like the correlation length, the susceptibility or the specific heat have singularities in the critical point. The goal is the precise temperature dependence near these singularities. A cooperative many particel effect generates critical behavior. Differences in the short range microscopic interaction of the investigated systems are insignificant. The dimension d and the number of components of the order parameter determine the critical behavior. The renormalization group theory identifies universality classes of critical behavior and predicts that critical exponents and certain amplitude ratios are equal for all systems of the same universality class. The case d=3, n=2 is of special interest. Experimental results of the superfluid transition of 4^He in space are compared to MC simulations of spin systems and analytical calculations in the framework of the phi^4 theory. This is a high precision test of the RG prediction of universality. RG theory has a wide range of applications. Hence, this quantitative test of RG is of interest in statistical physics, condensed matter physics and elementary particle physics. A short summary of two main results: A significant improvement of former Borel summations of critical exponents gamma and alpha is achieved with the same information of perturbation series. This improvement stems from an enhancement of the method of resummation. Amplitude functions at the fixpoint are resummed. Analytical results for certain universal amplitude ratios are achieved. So far only numerical or experimental quantitative results for these ratios are known."],"dc:identifier":["https://publications.rwth-aachen.de/record/50011","https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-112576%22"],"dc:language":["ger"],"dc:publisher":["Publikationsserver der RWTH Aachen University"],"dc:relation":["info:eu-repo/semantics/altIdentifier/urn/urn:nbn:de:hbz:82-opus-22522"],"dc:rights":["info:eu-repo/semantics/openAccess"],"dc:source":["Aachen : Publikationsserver der RWTH Aachen University 151 S. : graph. Darst. (2008). = Aachen, Techn. Hochsch., Diss., 2008"],"dc:subject":["info:eu-repo/classification/ddc/530","Physik","Phasenübergänge","kritische Exponenten","universelle Amplitudenverhältnisse","phase transitions","critical exponents","universal amplitude ratios"],"dc:title":["Optimierte Borelsummation von kritischen Exponenten und universellen Amplitudenverhältnissen im phi 4-Modell"],"dc:type":["info:eu-repo/semantics/doctoralThesis","info:eu-repo/semantics/publishedVersion"]},"updated_at":"2026-07-30T19:40:16Z"}