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    POTTS MODELS AND RELATED PROBLEMS IN STATISTICAL MECHANICS

    by Paul Martin (City University, London)

     
    Contents:
    • Introduction
    • Transfer Matrices: On Commuting Transfer Matrices
    • On Exactly Solved Cases
    • Algebra: General Principles
    • Temperley-Lieb Algebra: Generic Cases
    • Special Cases
    • Graph Temperley-Lieb Algebras
    • Hecke Algebras
    • Algebraic Formalism for ZQ Symmetry
    • The Modelling of Phase Transitions
    • Vertex Models and Related Algebras, Braids and Cables
     
    Readership: Mathematical physicists.
     
    “This is an excellent survey of the Potts model and related matters in statistical mechanics. The first chapter constitutes a good introduction to statistical mechanics with a discussion of modelling principles, partition functions and Hamiltonians, lattices, statistical mechanics functions such as free energy. There are good general discussions of phase transitions, order parameters and critical exponents. Then the Potts models are defined and related to dichromatic polynomials and to the special case of the Ising model. The chapter ends with a discussion of block spin renormalization … This book is a fine source of basic results about the Potts model and its mathematical physics environment.”
    Mathematical Reviews
     
    360pp    Pub. date: Feb 1991  
    ISBN:   978-981-02-0075-6
    981-02-0075-7
       US$53 / £35

     


    360pp    Pub. date: Feb 1991  
    ISBN:   978-981-4368-32-2(ebook)
    981-4368-32-6(ebook)
       US$69 / £46

     


     

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    Updated on 14 February 2012