The connection between statistical mechanics and quantum field theory

Abstract

A four part series of lectures on the connection of statistical mechanics and quantum field theory. The general principles relating statistical mechanics and the path integral formulation of quantum field theory are presented in the first lecture. These principles are then illustrated in lecture 2 by a presentation of the theory of the Ising model for $H=0$, where both the homogeneous and randomly inhomogeneous models are treated and the scaling theory and the relation with Fredholm determinants and Painlev{é} equations is presented. In lecture 3 we consider the Ising model with $H\ne 0$, where the relation with gauge theory is used to discuss the phenomenon of confinement. We conclude in the last lecture with a discussion of quantum spin diffusion in one dimensional chains and a presentation of the chiral Potts model which illustrates the physical effects that can occur when the Euclidean and Minkowski regions are not connected by an analytic continuation. (To be published as part of the Proceedings of the Sixth Annual Theoretical Physics Summer School of the Australian National University which was held in Canberra during Jan. 1994.)

94 pages in harvmac with 6 figures appended to the file, ITP-SB-94-07. (Several references have been added to part 2.)

Cited by in corpus (12)

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• Non-integrable Quantum Field Theories as Perturbations of Certain Integrable Models
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• Toeplitz determinants with merging singularities
• Spin matrix elements in 2D Ising model on the finite lattice
• Loop quantization as a continuum limit
• Fermionic Expressions for the Characters of c(p,1) Logarithmic Conformal Field Theories
• What the characters of irreducible subrepresentations of Jordan cells can tell us about LCFT
• Quantization of Fields by Averaging Classical Evolution Equations
• The Fisher-Hartwig Formula and Generalized Entropies in XY Spin Chain
• Slit-strip Ising boundary conformal field theory 2: Scaling limits of fusion coefficients
• Improved harmonic approximation and the 2D Ising model at $T\ne T_c$ and $h\ne 0$