I. Manolescu: Structure of Gibbs measures for planar FK-percolation and Potts models

Abstract: We study the Gibbs measures for the Potts and FK-percolation models on the square lattice. In both cases, the set of extremal Gibbs measures is known away from criticality, as well as at criticality when q is between 1 and 4.

Our work concerns the critical case for q above 4. For the Potts model, we prove that all Gibbs measures are linear combinations of the q+1 thermodynamic limits with free and monochromatic boundary conditions, respectively. For FK-percolation, all Gibbs measures are linear combinations of the free and wired infinite-volume measures.

The arguments are non-quantitative and follow the spirit of the seminal works of Aizenman and Higuchi, which established the Gibbs structure for the two-dimensional Ising model. Infinite-range dependencies in FK-percolation pose serious additional difficulties compared to the case of the Ising model.

Joint work with Alexander Glazman.


Password Protected

This video is password-protected. Please verify with a password to unlock the content.