Séminaire Lotharingien de Combinatoire, B73b (2015), 13 pp.
Ron Peled and Dan Romik
Bijective Combinatorial Proof of the Commutation of Transfer Matrices in the Dense O(1) Loop Model
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.
Received: February 17, 2015.
Accepted: February 24, 2015.
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