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.”
