Fisher renormalization of phase transitions

  • Jack Flanagan-Jones

    Student thesis: Master's ThesisMaster of Science by Research

    Abstract

    This thesis offers a full background to the subject of phase transitions and crit- ical phenomena through derivation and explanation of all relevant thermodynamic quantities, and the critical exponents and amplitudes that accompany them. Then, all universal quantities for ferromagnetic phase transition systems including scaling relations and amplitude relations are derived. Two paradigms of phase transition modeling - the one-dimensional and mean field Ising models - are fully evaluated. With a full background in place focus then turns to Fisher renormalization, where the critical exponents and amplitudes of a real system operating under constraint are derived from the ideal system. These exponents and amplitudes are then tested for involution, resulting in a discovery regarding the involutory nature of universal quantities that are fisher renormalized.
    Date of Award6 Aug 2010
    LanguageEnglish
    Awarding Institution
    • Coventry University

    Keywords

    • applied mathematics
    • statistics
    • statistical mechanics
    • phase transitions
    • thermodynamics
    • magnetism
    • ferromagnetism
    • Ising model
    • Ernst Ising
    • Michael Ellis Fisher
    • Fisher renormalization

    Cite this

    Fisher renormalization of phase transitions
    Flanagan-Jones, J. (Author). 6 Aug 2010

    Student thesis: Master's ThesisMaster of Science by Research