nLab
Ising model

Contents

Context

Algebraic Quantum Field Theory

algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)

Introduction

Concepts

field theory:

Lagrangian field theory

quantization

quantum mechanical system, quantum probability

free field quantization

gauge theories

interacting field quantization

renormalization

Theorems

States and observables

Operator algebra

Local QFT

Perturbative QFT

Functorial Quantum field theory

Contents

Idea

The Ising model is a simple model (in theoretical physics) of physical systems roughly similar to ferromagnets. Its configurations are functions on a lattice with values in {1,+1}\{-1,+1\}, roughly to be thought of as the magnetic polarizations of elementary magnets in a crystal lattice.

The Ising model gained importance as a toy model in theoretical physics. It is about the simplest possible model that allows methods of Euclidean quantum field theory in statistical physics and the study of critical phenomena?. In fact at a critical temperature and in dimension 2 the model exibits the behaviour of a 2dconformal field theory, one of the examples of rational conformal field theory.

Real-world physical systems that show behaviour described by the Ising model were only found later (Wolf).

Properties

References

  • Kasper Peeters, Marija Zamaklar, section 2.1 of Euclidean Field Theory, Lecture notes 2009-2011 (web, pdf)

  • W. P. Wolf, The Ising model and real magnetic materials, Braz. J. Phys. vol.30 no.4 São Paulo Dec. 2000 (web)

See also

Discussion of the Ising model 2d CFT as a boundary theory to a 3d TQFT based on the Turaev-Viro model, similar to the CS-WZW correspondence, and the phenomenon of Kramers-Wannier duality, is in:

(via FRS-formalism) and also in

3d version:

Last revised on April 8, 2019 at 04:53:13. See the history of this page for a list of all contributions to it.