• Admin
    UC Research Repository
    View Item 
       
    • UC Home
    • Library
    • UC Research Repository
    • College of Science
    • Science: Theses and Dissertations
    • View Item
       
    • UC Home
    • Library
    • UC Research Repository
    • College of Science
    • Science: Theses and Dissertations
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Browse

    All of the RepositoryCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

    Statistics

    View Usage Statistics

    Suppressing Discretization Error in Langevin Simulations of (2+1)-dimensional Field Theories

    Thumbnail
    View/Open
    thesis_fulltext.pdf (6.636Mb)
    Author
    Wojtas, David Heinrich
    Date
    2006
    Permanent Link
    http://hdl.handle.net/10092/1294
    Thesis Discipline
    Physics
    Degree Grantor
    University of Canterbury
    Degree Level
    Masters
    Degree Name
    Master of Science

    Lattice simulations are a popular tool for studying the non-perturbative physics of nonlinear field theories. To perform accurate lattice simulations, a careful account of the discretization error is necessary. Spatial discretization error as a result of lattice spacing dependence in Langevin simulations of anisotropic (2 + 1)-dimensional classical scalar field theories is studied. A transfer integral operator (TIO) method and a one-loop renormalization (1LR) procedure are used to formulate effective potentials. The effective potentials contain counterterms which are intended to suppress the lattice spacing dependence. The two effective potentials were tested numerically in the case of a phi-4 model. A high accuracy modified Euler method was used to evolve a phenomenological Langevin equation. Large scale Langevin simulations were performed in parameter ranges determined to be appropriate. Attempts at extracting correlation lengths as a means of determining effectiveness of each method were not successful. Lattice sizes used in this study were not of a sufficient size to obtain an accurate representation of thermal equilibrium. As an alternative, the initial behaviour of the ensemble field average was observed. Results for the TIO method showed that it was successful at suppressing lattice spacing dependence in a mean field limit. Results for the 1LR method showed that it performed poorly.

    Subjects
    quantum field theory
     
    Langevin simulations
     
    transfer matrix
     
    discretization
    Collections
    • Science: Theses and Dissertations [3604]
    Rights
    https://canterbury.libguides.com/rights/theses

    UC Research Repository
    University Library
    University of Canterbury
    Private Bag 4800
    Christchurch 8140

    Phone
    364 2987 ext 8718

    Email
    ucresearchrepository@canterbury.ac.nz

    Follow us
    FacebookTwitterYoutube

    © University of Canterbury Library
    Send Feedback | Contact Us