Exact densities of clusters in critical percolation and of loops in O(1) dense loop model on a cylinder of finite circumference.

Abstract: The percolation problem provides one of the basic examples of phase transition and critical behavior manifested in the statistics of percolation clusters. The critical bond percolation model on a square lattice is closely related to the $O(1)$ dense loop model, which, in turn, can be mapped on the exactly solvable six-vertex model at special values of the Boltzmann weights, known as the Razumov-Stroganov combinatorial point. This point is known for providing the possibility to obtain exact results in finite-size systems. I will review the latest results on calculating the exact densities of percolation clusters in critical percolation, as well as loops in the $O(1$) dense loop model on an infinite cylinder of a finite circumference.

mathematical physicsdynamical systemsquantum algebrarepresentation theorysymplectic geometry

Audience: general audience

( slides | video )

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BIMSA Integrable Systems Seminar

Series comments: The aim is to bring together experts in integrable systems and related areas of theoretical and mathematical physics and mathematics. There will be research presentations and overview talks.

Audience: Graduate students and researchers interested in integrable systems and related mathematical structures, such as symplectic and Poisson geometry and representation theory.

The zoom link will be distributed by mail, so please join the mailing list if you are interested in attending the seminar.

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