{"id":{"repo_id":"aachen","oai_identifier":"oai:publications.rwth-aachen.de:57223"},"canonical_url":"https://search.dev.ndltd.org/etd/aachen/oai:publications.rwth-aachen.de:57223","repository":{"repo_id":"aachen","name":"RWTH Aachen University","base_url":"https://publications.rwth-aachen.de/oai2d"},"display":{"title":"Magnetische Phasenübergänge im Hubbard-Modell mit Frustration","abstract":"In this thesis magnetic transitions accompanying the correlation-driven metal-insulator transition in the Hubbard Model with frustration are discussed. Spin systems are called frustrated if there are couplings between sites that hamper the transition to an antiferromagnetically ordered ground state. In the Hubbard Model this can be achieved by a proper choicee of the amplitudes between nearest and next nearest neighbors, generally called t and t'. In the case t'=0 one obtains an antiferromagnetically ordered ground state for every on-site interaction U. For small values of U magnetic symmetry breaking is found together with a metal-insulator transition. In the paramagnetic phase the system changes gradually with increasing U from the metallic to the insulating state. All magnetic transitions are of second order. In the case of finite t' the phase diagram is more complicated and, depending on the degree of frustration, one can find, in addition, first order transitions or more phases, e.g. an antiferromagnetic metal. The main focus of this thesis is on the perturbatively not accessible regions of intermediate coupling. The self-consistency equations for the Bethe lattice with infinite connectivity with finite t' and with total translational invariance are derived. Also, a new method to calculate the corresponding Green and correlation functions is found and solved by means of well-known Monte Carlo and dynamical mean field (DMFT) techniques. It is also discussed how thermodynamical variables depending on U and temperature are influenced by frustration and how the order of the magnetic transition could be changed from second to first order. From the present DMFT results it is concluded that for t'/t=0.5 and intermediate coupling a first order transition from the paramagnetic phase to antiferromagnetism occurs. For t'/t=0.75, even at higher coupling, no antiferromagnetic ordering was found.","abstract_html":"In this thesis magnetic transitions accompanying the correlation-driven metal-insulator transition in the Hubbard Model with frustration are discussed. Spin systems are called frustrated if there are couplings between sites that hamper the transition to an antiferromagnetically ordered ground state. In the Hubbard Model this can be achieved by a proper choicee of the amplitudes between nearest and next nearest neighbors, generally called t and t'. In the case t'=0 one obtains an antiferromagnetically ordered ground state for every on-site interaction U. For small values of U magnetic symmetry breaking is found together with a metal-insulator transition. In the paramagnetic phase the system changes gradually with increasing U from the metallic to the insulating state. All magnetic transitions are of second order. In the case of finite t' the phase diagram is more complicated and, depending on the degree of frustration, one can find, in addition, first order transitions or more phases, e.g. an antiferromagnetic metal. The main focus of this thesis is on the perturbatively not accessible regions of intermediate coupling. The self-consistency equations for the Bethe lattice with infinite connectivity with finite t' and with total translational invariance are derived. Also, a new method to calculate the corresponding Green and correlation functions is found and solved by means of well-known Monte Carlo and dynamical mean field (DMFT) techniques. It is also discussed how thermodynamical variables depending on U and temperature are influenced by frustration and how the order of the magnetic transition could be changed from second to first order. From the present DMFT results it is concluded that for t'/t=0.5 and intermediate coupling a first order transition from the paramagnetic phase to antiferromagnetism occurs. For t'/t=0.75, even at higher coupling, no antiferromagnetic ordering was found.","abstract_has_math":false,"creators":["Radke de Cuba, Maria Hedwig"],"institution":"Publikationsserver der RWTH Aachen University","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Metzner, Walter"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2002,"date_issued":"2002","date_published":"2002","updated_at":"2026-07-30T19:42:09Z","subjects":["info:eu-repo/classification/ddc/530","Physik","stark korrelierte Elektronensysteme"],"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-119280%22"],"render_values":[{"text":"https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-119280%22","href":"https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-119280%22","code":true}]}]},"links":{"outbound_url":"https://publications.rwth-aachen.de/record/57223","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Metzner, Walter"]},{"key":"dc:creator","label":"Author","values":["Radke de Cuba, Maria Hedwig"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:coverage","label":"Dc Coverage","values":["DE"]},{"key":"dc:date","label":"Dc Date","values":["2002"]},{"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-4628"]},{"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","stark korrelierte Elektronensysteme"]}]},{"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/57223","https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-119280%22"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In this thesis magnetic transitions accompanying the correlation-driven metal-insulator transition in the Hubbard Model with frustration are discussed. Spin systems are called frustrated if there are couplings between sites that hamper the transition to an antiferromagnetically ordered ground state. In the Hubbard Model this can be achieved by a proper choicee of the amplitudes between nearest and next nearest neighbors, generally called t and t'. In the case t'=0 one obtains an antiferromagnetically ordered ground state for every on-site interaction U. For small values of U magnetic symmetry breaking is found together with a metal-insulator transition. In the paramagnetic phase the system changes gradually with increasing U from the metallic to the insulating state. All magnetic transitions are of second order. In the case of finite t' the phase diagram is more complicated and, depending on the degree of frustration, one can find, in addition, first order transitions or more phases, e.g. an antiferromagnetic metal. The main focus of this thesis is on the perturbatively not accessible regions of intermediate coupling. The self-consistency equations for the Bethe lattice with infinite connectivity with finite t' and with total translational invariance are derived. Also, a new method to calculate the corresponding Green and correlation functions is found and solved by means of well-known Monte Carlo and dynamical mean field (DMFT) techniques. It is also discussed how thermodynamical variables depending on U and temperature are influenced by frustration and how the order of the magnetic transition could be changed from second to first order. From the present DMFT results it is concluded that for t'/t=0.5 and intermediate coupling a first order transition from the paramagnetic phase to antiferromagnetism occurs. For t'/t=0.75, even at higher coupling, no antiferromagnetic ordering was found."]},{"key":"dc:source","label":"Dc Source","values":["Aachen : Publikationsserver der RWTH Aachen University 153 S. : graph. Darst. (2002). = Aachen, Techn. Hochsch., Diss., 2002"]},{"key":"dc:title","label":"Title","values":["Magnetische Phasenübergänge im Hubbard-Modell mit Frustration"]}]}],"canonical_facts":{"dc:contributor":["Metzner, Walter"],"dc:coverage":["DE"],"dc:creator":["Radke de Cuba, Maria Hedwig"],"dc:date":["2002"],"dc:description":["In this thesis magnetic transitions accompanying the correlation-driven metal-insulator transition in the Hubbard Model with frustration are discussed. Spin systems are called frustrated if there are couplings between sites that hamper the transition to an antiferromagnetically ordered ground state. In the Hubbard Model this can be achieved by a proper choicee of the amplitudes between nearest and next nearest neighbors, generally called t and t'. In the case t'=0 one obtains an antiferromagnetically ordered ground state for every on-site interaction U. For small values of U magnetic symmetry breaking is found together with a metal-insulator transition. In the paramagnetic phase the system changes gradually with increasing U from the metallic to the insulating state. All magnetic transitions are of second order. In the case of finite t' the phase diagram is more complicated and, depending on the degree of frustration, one can find, in addition, first order transitions or more phases, e.g. an antiferromagnetic metal. The main focus of this thesis is on the perturbatively not accessible regions of intermediate coupling. The self-consistency equations for the Bethe lattice with infinite connectivity with finite t' and with total translational invariance are derived. Also, a new method to calculate the corresponding Green and correlation functions is found and solved by means of well-known Monte Carlo and dynamical mean field (DMFT) techniques. It is also discussed how thermodynamical variables depending on U and temperature are influenced by frustration and how the order of the magnetic transition could be changed from second to first order. From the present DMFT results it is concluded that for t'/t=0.5 and intermediate coupling a first order transition from the paramagnetic phase to antiferromagnetism occurs. For t'/t=0.75, even at higher coupling, no antiferromagnetic ordering was found."],"dc:identifier":["https://publications.rwth-aachen.de/record/57223","https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-119280%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-4628"],"dc:rights":["info:eu-repo/semantics/openAccess"],"dc:source":["Aachen : Publikationsserver der RWTH Aachen University 153 S. : graph. Darst. (2002). = Aachen, Techn. Hochsch., Diss., 2002"],"dc:subject":["info:eu-repo/classification/ddc/530","Physik","stark korrelierte Elektronensysteme"],"dc:title":["Magnetische Phasenübergänge im Hubbard-Modell mit Frustration"],"dc:type":["info:eu-repo/semantics/doctoralThesis","info:eu-repo/semantics/publishedVersion"]},"updated_at":"2026-07-30T19:42:09Z"}