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BIMSA Integrable Systems Seminar
Exact densities of clusters in critical percolation and of loops in O(1) dense loop model on a cylinder of finite circumference.
Exact densities of clusters in critical percolation and of loops in O(1) dense loop model on a cylinder of finite circumference.
Organizers
Speaker
Alexander Povolotsky
Time
Tuesday, October 22, 2024 4:00 PM - 5:00 PM
Venue
A6-101
Online
Zoom 873 9209 0711
(BIMSA)
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.