Name:
azu_etd_10709_sip1_m.pdf
Size:
838.1Kb
Format:
PDF
Description:
azu_etd_10709_sip1_m.pdf
Author
Hystad, GretheIssue Date
2009Keywords
B. KaufmanBugrij-Lisovyy conjecture for spin matrix elements
Periodic two-dimensional Ising Model
Scaling limit of multi-spin Ising correlations
Spin Correlation function
Spin matrix elements
Advisor
Palmer, John NCommittee Chair
Palmer, John N
Metadata
Show full item recordPublisher
The University of Arizona.Rights
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.Abstract
We consider the finite two-dimensional Ising model on a lattice with periodic boundaryconditions. Kaufman determined the spectrum of the transfer matrix on the finite,periodic lattice, and her derivation was a simplification of Onsager's famous result onsolving the two-dimensional Ising model. We derive and rework Kaufman's resultsby applying representation theory, which give us a more direct approach to computethe spectrum of the transfer matrix. We determine formulas for the spin correlationfunction that depend on the matrix elements of the induced rotation associated withthe spin operator. The representation of the spin matrix elements is obtained byconsidering the spin operator as an intertwining map. We wrap the lattice aroundthe cylinder taking the semi-infinite volume limit. We control the scaling limit of themulti-spin Ising correlations on the cylinder as the temperature approaches the criticaltemperature from below in terms of a Bugrij-Lisovyy conjecture for the spin matrixelements on the finite, periodic lattice. Finally, we compute the matrix representationof the spin operator for temperatures below the critical temperature in the infinite-volume limit in the pure state defined by plus boundary conditions.Type
textElectronic Dissertation
Degree Name
Ph.D.Degree Level
doctoralDegree Program
MathematicsGraduate College