Bijective combinatorial proof of the commutation of transfer matrices in the dense O(1) loop model
Mathematical Physics
2017-03-14 v1 Combinatorics
math.MP
Probability
Abstract
The dense O(1) loop model is a statistical physics model with connections to the quantum XXZ spin chain, alternating sign matrices, the six-vertex model and critical bond percolation on the square lattice. When cylindrical boundary conditions are imposed, the model possesses a commuting family of transfer matrices. The original proof of the commutation property is algebraic and is based on the Yang-Baxter equation. In this paper we give a new proof of this fact using a direct combinatorial bijection.
Keywords
Cite
@article{arxiv.1407.5357,
title = {Bijective combinatorial proof of the commutation of transfer matrices in the dense O(1) loop model},
author = {Ron Peled and Dan Romik},
journal= {arXiv preprint arXiv:1407.5357},
year = {2017}
}
Comments
18 pages, many figures