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    Witten Laplacian Methods For Critical Phenomena

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    Author
    Lo, Assane
    Issue Date
    2007
    Keywords
    Witten Laplacians
    Correlations
    Analyticity
    Pressure
    Advisor
    Pinson, Haru
    Committee Chair
    Pinson, Haru
    
    Metadata
    Show full item record
    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
    Degree Name
    PhD
    Degree Level
    doctoral
    Degree Program
    Mathematics
    Graduate College
    Degree Grantor
    University of Arizona
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