On the partition function for the three-dimensional Ising model

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.

Name dc:type.qualificationname

phd

Level dc:type.qualificationlevel

doctoral

Grantor dc:publisher.institution

City University London

Year dc:date.issued

2011

Author dc:creator

• Valani, Y.P.

• TA Engineering (General). Civil engineering (General)