Local Statistics of Realizable Vertex Models

Details Local Statistics of Realizable Vertex Models Local Statistics of Realizable Vertex Models

2010-06-19

arxiv.org/abs/1006.3842v1

Communications in Mathematical Physics, Volume 304, Number 3, 723-763, 2011

Physics

Mathematical Physics

Scientific paper

10.1007/s00220-011-1240-y

We study planar "vertex" models, which are probability measures on edge subsets of a planar graph, satisfying certain constraints at each vertex, examples including dimer model, and 1-2 model, which we will define. We express the local statistics of a large class of vertex models on a finite hexagonal lattice as a linear combination of the local statistics of dimers on the corresponding Fisher graph, with the help of a generalized holographic algorithm. Using an $n\times n$ torus to approximate the periodic infinite graph, we give an explicit integral formula for the free energy and local statistics for configurations of the vertex model on an infinite bi-periodic graph. As an example, we simulate the 1-2 model by the technique of Glauber dynamics.

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