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

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.

Received: February 17, 2015. Accepted: February 24, 2015.

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