Persistent Link:
http://hdl.handle.net/10150/196130
Title:
Periodic Ising Correlations
Author:
Hystad, Grethe
Issue Date:
2009
Publisher:
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:
text; Electronic Dissertation
Keywords:
B. Kaufman; Bugrij-Lisovyy conjecture for spin matrix elements; Periodic two-dimensional Ising Model; Scaling limit of multi-spin Ising correlations; Spin Correlation function; Spin matrix elements
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Mathematics; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Palmer, John N
Committee Chair:
Palmer, John N

Full metadata record

DC FieldValue Language
dc.language.isoENen_US
dc.titlePeriodic Ising Correlationsen_US
dc.creatorHystad, Gretheen_US
dc.contributor.authorHystad, Gretheen_US
dc.date.issued2009en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © 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.en_US
dc.description.abstractWe 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.en_US
dc.typetexten_US
dc.typeElectronic Dissertationen_US
dc.subjectB. Kaufmanen_US
dc.subjectBugrij-Lisovyy conjecture for spin matrix elementsen_US
dc.subjectPeriodic two-dimensional Ising Modelen_US
dc.subjectScaling limit of multi-spin Ising correlationsen_US
dc.subjectSpin Correlation functionen_US
dc.subjectSpin matrix elementsen_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorPalmer, John Nen_US
dc.contributor.chairPalmer, John Nen_US
dc.contributor.committeememberKennedy, Thomas Gen_US
dc.contributor.committeememberWatkins, Joseph Cen_US
dc.contributor.committeememberPickrell, Douglas Men_US
dc.identifier.proquest10709en_US
dc.identifier.oclc659753496en_US
All Items in UA Campus Repository are protected by copyright, with all rights reserved, unless otherwise indicated.