{"id":{"repo_id":"city-london","oai_identifier":"oai:openaccess.city.ac.uk:7793"},"canonical_url":"https://search.dev.ndltd.org/etd/city-london/oai:openaccess.city.ac.uk:7793","repository":{"repo_id":"city-london","name":"City University of London","base_url":"https://openaccess.city.ac.uk/cgi/oai2"},"display":{"title":"On the partition function for the three-dimensional Ising model","abstract":"Our aim is to investigate the critical behaviour of lattice spin models such as the three-dimensional Ising model in the thermodynamic limit. The exact partition functions (typically summed over the order of 1075 states) for finite simple cubic Ising lattices are computed using a transfer matrix approach. Q-state Potts model partition functions on two- and three-dimensional lattices are also computed and analysed. Our results are analysed as distributions of zeros of the partition function in the complex-temperature plane. We then look at sequences of such distributions for sequences of lattices approaching the thermodynamic limit. For a controlled comparison, we show how a sequence of zero distributions for finite 2d Ising lattices tends to Onsager’s thermodynamic solution. Via such comparisons, we find evidence to suggest, for example, a thermodynamic limit singular point in the behaviour of the specific heat of the 3d Ising model.","abstract_html":"Our aim is to investigate the critical behaviour of lattice spin models such as the three-dimensional Ising model in the thermodynamic limit. The exact partition functions (typically summed over the order of 1075 states) for finite simple cubic Ising lattices are computed using a transfer matrix approach. Q-state Potts model partition functions on two- and three-dimensional lattices are also computed and analysed. Our results are analysed as distributions of zeros of the partition function in the complex-temperature plane. We then look at sequences of such distributions for sequences of lattices approaching the thermodynamic limit. For a controlled comparison, we show how a sequence of zero distributions for finite 2d Ising lattices tends to Onsager’s thermodynamic solution. Via such comparisons, we find evidence to suggest, for example, a thermodynamic limit singular point in the behaviour of the specific heat of the 3d Ising model.","abstract_has_math":false,"creators":["Valani, Y.P."],"institution":"City University London","degree_name":"phd","degree_level":"doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-08","date_published":"2011-08","updated_at":"2026-07-24T01:39:04Z","subjects":["TA Engineering (General). 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We then look at sequences of such distributions for sequences of lattices approaching the thermodynamic limit. For a controlled comparison, we show how a sequence of zero distributions for finite 2d Ising lattices tends to Onsager’s thermodynamic solution. Via such comparisons, we find evidence to suggest, for example, a thermodynamic limit singular point in the behaviour of the specific heat of the 3d Ising model."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["On the partition function for the three-dimensional Ising model"]}]}],"canonical_facts":{"dc:creator":["Valani, Y.P."],"dc:date":["2011-08"],"dc:date.issued":["2011-08"],"dc:description.abstract":["Our aim is to investigate the critical behaviour of lattice spin models such as the three-dimensional Ising model in the thermodynamic limit. The exact partition functions (typically summed over the order of 1075 states) for finite simple cubic Ising lattices are computed using a transfer matrix approach. Q-state Potts model partition functions on two- and three-dimensional lattices are also computed and analysed. Our results are analysed as distributions of zeros of the partition function in the complex-temperature plane. We then look at sequences of such distributions for sequences of lattices approaching the thermodynamic limit. For a controlled comparison, we show how a sequence of zero distributions for finite 2d Ising lattices tends to Onsager’s thermodynamic solution. Via such comparisons, we find evidence to suggest, for example, a thermodynamic limit singular point in the behaviour of the specific heat of the 3d Ising model."],"dc:format":["application/pdf"],"dc:identifier.uri":["https://openaccess.city.ac.uk/id/eprint/7793/1/On_the_partition_function_for_the_three-dimensional_Ising_Model.pdf"],"dc:publisher.department":["Department of Mathematics","Doctoral Theses","School of Science & Technology Doctoral Theses","Engineering and Mathematical Sciences"],"dc:publisher.institution":["City University London"],"dc:relation.isreferencedby":["https://openaccess.city.ac.uk/id/eprint/7793/"],"dc:subject":["TA Engineering (General). Civil engineering (General)"],"dc:title":["On the partition function for the three-dimensional Ising model"],"dc:type":["Thesis"],"dc:type.qualificationlevel":["doctoral"],"dc:type.qualificationname":["phd"]},"updated_at":"2026-07-24T01:39:04Z"}