Symbolic solution and microcanonical simulation of the Potts model.
Date
1994
Authors
Frempong-Mireku, Peter.
Journal Title
Journal ISSN
Volume Title
Publisher
Dalhousie University
Abstract
Description
An analysis of the Ising-Potts model using symbolic computation is presented. The work considers the Kramers and Wannier V-matrix in two-dimensions and its extension to three-dimensions. Some of the properties of the V-matrices are also considered. The computation of the partition function of Potts-Ising model is carried out using the perturbation theory. The computation of the partition function has been completed on a two dimensional square net and on a three-dimensional cubic lattice as well. The eigenvectors needed to analyze the propagation of order in the crystal, and to compute long-range order in crystals have been given. An Onsager complete solution for the two-dimensional model has been incorporated as well as the two-dimensional n-state Potts model. A construction of symbolic proof that a order-disorder transition actually takes place in crystal has also been considered. The computation of the ground state entropy which provides a formal connection to the coloring of graphs has been examined.
The second part of the thesis examines the three-state Potts model on a three-dimensional cubic lattice. Using the microcanonical simulation method, the dynamic critical exponent z and the critical exponent v were measured to be z = 2.11 $\pm$ 0.05 and v = 0.613 $\pm$ 0.005 respectively. Also a general theorem for computing the average demon energy and an important consequence of the theorem has been presented.
Thesis (Ph.D.)--Dalhousie University (Canada), 1994.
The second part of the thesis examines the three-state Potts model on a three-dimensional cubic lattice. Using the microcanonical simulation method, the dynamic critical exponent z and the critical exponent v were measured to be z = 2.11 $\pm$ 0.05 and v = 0.613 $\pm$ 0.005 respectively. Also a general theorem for computing the average demon energy and an important consequence of the theorem has been presented.
Thesis (Ph.D.)--Dalhousie University (Canada), 1994.
Keywords
Mathematics.