Persistent Link:
http://hdl.handle.net/10150/193872
Title:
Witten Laplacian Methods For Critical Phenomena
Author:
Lo, Assane
Issue Date:
2007
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:
It is well known that very few models of interacting systems particularly those in dimension higher than two, can be solved exactly. The mean-field treatment is the first step in approximate calculations for such models. Although mean-field approximation leads to sufficiently accurate results of the thermodynamic properties of these systems away from critical points, most often it fails miserably close to the critical points. In this thesis, we propose to study direct methods (not based on any mean-field type approximations) for proving the exponential decay of the two point-correlation functions and the analyticity of the pressure (free energy per unit volume) for models of Kac type. The methods are based on the Helffer-Sjöstrand formula for the covariance in terms of Witten's Laplacians.
Type:
text; Electronic Dissertation
Keywords:
Witten Laplacians; Correlations; Analyticity; Pressure
Degree Name:
PhD
Degree Level:
doctoral
Degree Program:
Mathematics; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Pinson, Haru
Committee Chair:
Pinson, Haru

Full metadata record

DC FieldValue Language
dc.language.isoENen_US
dc.titleWitten Laplacian Methods For Critical Phenomenaen_US
dc.creatorLo, Assaneen_US
dc.contributor.authorLo, Assaneen_US
dc.date.issued2007en_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.abstractIt is well known that very few models of interacting systems particularly those in dimension higher than two, can be solved exactly. The mean-field treatment is the first step in approximate calculations for such models. Although mean-field approximation leads to sufficiently accurate results of the thermodynamic properties of these systems away from critical points, most often it fails miserably close to the critical points. In this thesis, we propose to study direct methods (not based on any mean-field type approximations) for proving the exponential decay of the two point-correlation functions and the analyticity of the pressure (free energy per unit volume) for models of Kac type. The methods are based on the Helffer-Sjöstrand formula for the covariance in terms of Witten's Laplacians.en_US
dc.typetexten_US
dc.typeElectronic Dissertationen_US
dc.subjectWitten Laplaciansen_US
dc.subjectCorrelationsen_US
dc.subjectAnalyticityen_US
dc.subjectPressureen_US
thesis.degree.namePhDen_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorPinson, Haruen_US
dc.contributor.chairPinson, Haruen_US
dc.contributor.committeememberPinson, Haruen_US
dc.contributor.committeememberErcolani, Nicholas M.en_US
dc.contributor.committeememberWatkins, Joseph C.en_US
dc.contributor.committeememberKennedy, Thomas G.en_US
dc.identifier.proquest2024en_US
dc.identifier.oclc659746621en_US
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