Celebratio Mathematica — Jones

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V. F. R. Jones: “Notes on subfactors and statistical mechanics,” pp. 1–25 in Braid group, knot theory and statistical mechanics, II. Edited by C. N. Yang and M. L. Ge. Advanced Series in Mathematical Physics 9. World Scientific (River Edge, NJ), 1989. Also published in Int. J. Mod. Phys. A 5:3 (1990) and Braid group, knot theory and statistical mechanics, II (1994). MR 1062421 Zbl 0725.46038 incollection

A lot has been made in the last few years of connections between knot theory, statistical mechanics, field theory and von Neumann algebras. Because of their more technical nature, the von Neumann algebras have tended to be neglected in surveys. This is not an accurate reflection of their fundamental role in the subject, both as a continuing inspiration and as the vehicle of the discovery of the original ties between statistical mechanics and knot theory. In this largely expository article, we attempt to redress this balance by talking almost entirely about Neumann algebras and prove they occur as algebras of transfer matrices in statistical mechanical models. We shall focus mostly on the Potts model and the model of Fateev and Zamolodchikov, with a brief exposition of how vertex models are related to type \( \mathrm{III} \) factors.

Mo Lin Ge	Related
Chen Ning Yang	Related

V. F. R. Jones: “Notes on subfactors and statistical mechanics,” pp. 177–201 in Braid group, knot theory and statistical mechanics, II. Edited by C. N. Yang and M. L. Ge. Advanced Series in Mathematical Physics 17. World Scientific (River Edge, NJ), 1994. Also published in Braid group, knot theory and statistical mechanics, II (1989) and Int. J. Mod. Phys. A 5:3 (1990). MR 1338603 Zbl 0822.46074 incollection

Mo Lin Ge	Related
Chen Ning Yang	Related