Use this URL to cite or link to this record in EThOS: | https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.546769 |
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Title: | On the partition function for the three-dimensional Ising model | ||||||
Author: | Valani, Yogendra P. |
ISNI:
0000 0004 2711 3689
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Awarding Body: | City University London | ||||||
Current Institution: | City, University of London | ||||||
Date of Award: | 2011 | ||||||
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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.
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Supervisor: | Not available | Sponsor: | Not available | ||||
Qualification Name: | Thesis (Ph.D.) | Qualification Level: | Doctoral | ||||
EThOS ID: | uk.bl.ethos.546769 | DOI: | Not available | ||||
Keywords: | TA Engineering (General). Civil engineering (General) | ||||||
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