{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/30673"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/30673","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Energy density correlations in the three-dimensional Ising model","abstract":"The energy-density-energy-density correlation function is studied in the three-dimensional Ising model in zero external field, for various spins on the fcc lattice. An extension of the linked-cluster technique is used to obtain high-temperature series expansions for the correlation function and its associated functions, to at least eighth order in the high-temperature interaction variable. Analysis of the series provides values for their critical indices and amplitudes. These values are used to verify the predictions of several theories of critical behavior. The critical index of the coherence length of the energy density correlation function is found to be equal to that of the spin-spin correlation function for all spins within the accuracy obtained here. For spins higher than ~ this critical index appears to obey strong scaling. An analysis of universality indicates that only one scale factor is needed to transform the energy density correlation function from one spin to another. This prediction is checked here and found to be good within our present accuracy. The current-algebra hypothesis predicts definite relations between the leading singularities of various correlation functions at the critical point. This prediction is checked directly and consistent values of the leading coefficients are obtained. The shape of the energy density correlation function at large distances from the origin, both at and above the critical point, is determined. The results are sufficiently accurate to rule out the Ornstein-Zernike form in zero field for T > T , but not sufficient to eliminate the possibility c of anisotropy at T = T .","abstract_html":"The energy-density-energy-density correlation function is studied in the three-dimensional Ising model in zero external field, for various spins on the fcc lattice. An extension of the linked-cluster technique is used to obtain high-temperature series expansions for the correlation function and its associated functions, to at least eighth order in the high-temperature interaction variable. Analysis of the series provides values for their critical indices and amplitudes. These values are used to verify the predictions of several theories of critical behavior. The critical index of the coherence length of the energy density correlation function is found to be equal to that of the spin-spin correlation function for all spins within the accuracy obtained here. For spins higher than ~ this critical index appears to obey strong scaling. An analysis of universality indicates that only one scale factor is needed to transform the energy density correlation function from one spin to another. This prediction is checked here and found to be good within our present accuracy. The current-algebra hypothesis predicts definite relations between the leading singularities of various correlation functions at the critical point. This prediction is checked directly and consistent values of the leading coefficients are obtained. The shape of the energy density correlation function at large distances from the origin, both at and above the critical point, is determined. The results are sufficiently accurate to rule out the Ornstein-Zernike form in zero field for T > T , but not sufficient to eliminate the possibility c of anisotropy at T = T .","abstract_has_math":false,"creators":["Rutherford, Reginald"],"institution":null,"degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":["M. Wortis"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012-04-19T18:41:58Z","date_published":"2012-04-19T18:41:58Z","updated_at":"2026-07-22T22:25:29Z","subjects":["energy density correlation function","Ising model","phase transitions","face-centered cubic lattice"],"languages":["en"],"rights":["© 1973 Reginald Rutherford"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["2596096"],"render_values":[{"text":"2596096","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/30673","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["M. 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An extension of the linked-cluster technique is used to obtain high-temperature series expansions for the correlation function and its associated functions, to at least eighth order in the high-temperature interaction variable. Analysis of the series provides values for their critical indices and amplitudes. These values are used to verify the predictions of several theories of critical behavior. The critical index of the coherence length of the energy density correlation function is found to be equal to that of the spin-spin correlation function for all spins within the accuracy obtained here. For spins higher than ~ this critical index appears to obey strong scaling. An analysis of universality indicates that only one scale factor is needed to transform the energy density correlation function from one spin to another. This prediction is checked here and found to be good within our present accuracy. The current-algebra hypothesis predicts definite relations between the leading singularities of various correlation functions at the critical point. This prediction is checked directly and consistent values of the leading coefficients are obtained. The shape of the energy density correlation function at large distances from the origin, both at and above the critical point, is determined. The results are sufficiently accurate to rule out the Ornstein-Zernike form in zero field for T > T , but not sufficient to eliminate the possibility c of anisotropy at T = T .","Submitted by Megan O'Donnell (mnodonn2@illinois.edu) on 2012-04-19T18:41:58Z No. of bitstreams: 1 1973_rutherford.pdf: 4190118 bytes, checksum: 55f028c488e0b3523c6025bc843fd790 (MD5)","Made available in DSpace on 2012-04-19T18:41:58Z (GMT). No. of bitstreams: 1 1973_rutherford.pdf: 4190118 bytes, checksum: 55f028c488e0b3523c6025bc843fd790 (MD5) Previous issue date: 1973","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Megan O'Donnell (mnodonn2@illinois.edu) on 2012-04-19T18:41:58Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:34:41-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: thesis/dissertation","thesis/dissertation","U of I Only"]},{"key":"dc:title","label":"Title","values":["Energy density correlations in the three-dimensional Ising model"]}]}],"canonical_facts":{"dc:contributor":["M. Wortis"],"dc:creator":["Rutherford, Reginald"],"dc:date":["2012-04-19T18:41:58Z","10000-01-01","1973"],"dc:description":["The energy-density-energy-density correlation function is studied in the three-dimensional Ising model in zero external field, for various spins on the fcc lattice. An extension of the linked-cluster technique is used to obtain high-temperature series expansions for the correlation function and its associated functions, to at least eighth order in the high-temperature interaction variable. Analysis of the series provides values for their critical indices and amplitudes. These values are used to verify the predictions of several theories of critical behavior. The critical index of the coherence length of the energy density correlation function is found to be equal to that of the spin-spin correlation function for all spins within the accuracy obtained here. For spins higher than ~ this critical index appears to obey strong scaling. An analysis of universality indicates that only one scale factor is needed to transform the energy density correlation function from one spin to another. This prediction is checked here and found to be good within our present accuracy. The current-algebra hypothesis predicts definite relations between the leading singularities of various correlation functions at the critical point. This prediction is checked directly and consistent values of the leading coefficients are obtained. The shape of the energy density correlation function at large distances from the origin, both at and above the critical point, is determined. The results are sufficiently accurate to rule out the Ornstein-Zernike form in zero field for T > T , but not sufficient to eliminate the possibility c of anisotropy at T = T .","Submitted by Megan O'Donnell (mnodonn2@illinois.edu) on 2012-04-19T18:41:58Z No. of bitstreams: 1 1973_rutherford.pdf: 4190118 bytes, checksum: 55f028c488e0b3523c6025bc843fd790 (MD5)","Made available in DSpace on 2012-04-19T18:41:58Z (GMT). No. of bitstreams: 1 1973_rutherford.pdf: 4190118 bytes, checksum: 55f028c488e0b3523c6025bc843fd790 (MD5) Previous issue date: 1973","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Megan O'Donnell (mnodonn2@illinois.edu) on 2012-04-19T18:41:58Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:34:41-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: thesis/dissertation","thesis/dissertation","U of I Only"],"dc:identifier":["2596096","http://hdl.handle.net/2142/30673"],"dc:language":["en"],"dc:rights":["© 1973 Reginald Rutherford"],"dc:subject":["energy density correlation function","Ising model","phase transitions","face-centered cubic lattice"],"dc:title":["Energy density correlations in the three-dimensional Ising model"],"dc:type":["Dissertation / Thesis","text"],"thesis:degree_discipline":["Physics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."]},"updated_at":"2026-07-22T22:25:29Z"}