# nLab Ising model

Contents

### Context

#### Functorial Quantum field theory

functorial quantum field theory

# Contents

## Idea

The Ising model is a simple lattice model (in theoretical physics) of physical systems roughly similar to ferromagnets. Its configurations are functions on a lattice with values in $\{-1,+1\}$, 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).

## References

Original articles:

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Review:

• 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)