On the partition function for the three-dimensional Ising model

Valani, Y.P. (2011). On the partition function for the three-dimensional Ising model. (Unpublished Doctoral thesis, City University London)

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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.

Item Type: Thesis (Doctoral)
Subjects: T Technology > TA Engineering (General). Civil engineering (General)
Divisions: School of Engineering & Mathematical Sciences
URI: http://openaccess.city.ac.uk/id/eprint/11667

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