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**Notes on subfactors and statistical mechanics.**
*(English)*
Zbl 0822.46074

Yang, Chen Ning (ed.) et al., Braid group, knot theory and statistical mechanics II. London: World Scientific. Adv. Ser. Math. Phys. 17, 177-201 (1994).

A lot has been made in the last few years of connections between knot theory, statistical mechancis, field theory and von Neumann algebras. Because on their more technical nature, the von Neumann algebras have tended to be neglected. 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 von Neumann algebras and how they occur as algebras of transfer matrices in statistical mechanical models. We 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 III factors.

For the entire collection see [Zbl 0798.00007].

For the entire collection see [Zbl 0798.00007].

### MSC:

46L37 | Subfactors and their classification |

82B20 | Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics |

82B10 | Quantum equilibrium statistical mechanics (general) |