TY - BOOK ID - 213660 TI - Planar Ising Correlations PY - 2007 SN - 0817646205 PB - Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, DB - UniCat KW - Ising model. KW - Scaling laws (Statistical physics) KW - Ratio and proportion (Statistical physics) KW - Scale invariance (Statistical physics) KW - Scaling hypothesis (Statistical physics) KW - Scaling phenomena (Statistical physics) KW - Physical laws KW - Ranking and selection (Statistics) KW - Statistical physics KW - Lenz-Ising model KW - Ferromagnetism KW - Phase transformations (Statistical physics) KW - Mathematics. KW - Mathematical physics. KW - Statistical physics. KW - Applications of Mathematics. KW - Complex Systems. KW - Mathematical Methods in Physics. KW - Statistical Physics and Dynamical Systems. KW - Physics KW - Mathematical statistics KW - Physical mathematics KW - Math KW - Science KW - Statistical methods KW - Mathematics KW - Applied mathematics. KW - Engineering mathematics. KW - Dynamical systems. KW - Physics. KW - Natural philosophy KW - Philosophy, Natural KW - Physical sciences KW - Dynamics KW - Dynamical systems KW - Kinetics KW - Mechanics, Analytic KW - Force and energy KW - Mechanics KW - Statics KW - Engineering KW - Engineering analysis KW - Mathematical analysis UR - https://www.unicat.be/uniCat?func=search&query=sysid:213660 AB - 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. ER -