Planar Ising Correlations

ISBN-13: 9780817642488 / Angielski / Twarda / 2007 / 372 str.

John Palmer

Opis

This book examines in detail the correlations for the two-dimensional Ising model in the infinite volume or thermodynamic limit and the sub- and super- critical continuum scaling limits. Steady progress in recent years has been made in understanding the special mathematical features of certain exactly solvable models in statistical mechanics and quantum field theory, including the scaling limits of the 2-D Ising (lattice) model, and more generally, a class of 2-D quantum fields known as holonomic fields. New results have made it possible to obtain a detailed nonperturbative analysis of the multi-spin correlations. In particular, the book focuses on deformation analysis of the scaling functions of the Ising model. This self-contained work also includes discussions on Pfaffians, elliptic uniformization, the Grassmann calculus for spin representations, Weiner--Hopf factorization, determinant bundles, and monodromy preserving deformations. This work explores the Ising model as a microcosm of the confluence of interesting ideas in mathematics and physics, and will appeal to graduate students, mathematicians, and physicists interested in the mathematics of statistical mechanics and quantum field theory.

Spis treści

Preface * I. Ising Model on a Finite Square Lattice * II. Infinite Volume Limits * III. Scaling Limits * IV. Monodromy Preserving Deformations of the Euclidean Dirac Equation * V. Analysis of Tau Functions VI. Holonomic Quantum Fields * Appendix: Infinite Dimensional Spin Groups * Bibliography * Index