The connection between statistical mechanics and quantum field theory

TL;DR

This series of lectures explores the deep connections between statistical mechanics and quantum field theory, illustrating principles through models like the Ising model and discussing phenomena such as confinement and quantum spin diffusion.

Contribution

It provides a comprehensive overview of the relationship between statistical mechanics and quantum field theory, including new insights into models like the Ising and chiral Potts models.

Findings

Relation of statistical mechanics to path integrals in quantum field theory

Scaling theory and connections to Fredholm determinants and Painlevé equations

Discussion of confinement and quantum spin diffusion phenomena

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{\'e} equations is presented. In lecture 3 we consider the Ising model with $H\neq 0$, 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.)