On the integrability of the square-triangle random tiling model

Details On the integrability of the square-triangle random tiling model On the integrability of the square-triangle random tiling model

1996-11-07

arxiv.org/abs/solv-int/9611005v1

Phys. Rev. E 55, 3926 (1997)

Physics

Condensed Matter

Statistical Mechanics

11 pages, LaTeX, inluding 2 postscript figures

Scientific paper

10.1103/PhysRevE.55.3926

It is shown that the square-triangle random tiling model is equivalent to an asymmetric limit of the three colouring model on the honeycomb lattice. The latter model is known to be the O(n) model at T=0 and corresponds to the integrable model connected to the affine $A_2^{(1)}$ Lie algebra. Thus it is shown that the weights of the square-triangle random tiling satisfy the Yang-Baxter equation, albeit in a singular limit of a more general model. The three colouring model for general vertex weights is solved by algebraic Bethe Ansatz.

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