City Research Online

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 (Unpublished Doctoral thesis, City University London)


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.

Publication Type: Thesis (Doctoral)
Subjects: T Technology > TA Engineering (General). Civil engineering (General)
Departments: School of Science & Technology > Mathematics
Doctoral Theses
School of Science & Technology > School of Science & Technology Doctoral Theses
[thumbnail of On_the_partition_function_for_the_three-dimensional_Ising_Model.pdf]
PDF - Accepted Version
Download (2MB) | Preview


Add to AnyAdd to TwitterAdd to FacebookAdd to LinkedinAdd to PinterestAdd to Email


Downloads per month over past year

View more statistics

Actions (login required)

Admin Login Admin Login