algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)
quantum mechanical system, quantum probability
interacting field quantization
functorial quantum field theory
Reshetikhin?Turaev model? / Chern-Simons theory
FQFT and cohomology
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).
Potts model?
Original articles:
Franz Wegner, Duality in Generalized Ising Models and Phase Transitions without Local Order Parameters, Journal of Mathematical Physics 12, 2259 (1971) (doi:10.1063/1.1665530)
(introducing the idea of lattice QCD)
(…)
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)
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 March 29, 2021 at 00:37:34. See the history of this page for a list of all contributions to it.