dorsal/arxiv
View SchemaOn the integrability of the square-triangle random tiling model
| Authors | Jan de Gier, Bernard Nienhuis |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9611005 |
| URL | https://arxiv.org/abs/solv-int/9611005 |
| DOI | 10.1103/PhysRevE.55.3926 |
| Journal | Phys. Rev. E 55, 3926 (1997) |
Abstract
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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"abstract": "It is shown that the square-triangle random tiling model is equivalent to an\nasymmetric limit of the three colouring model on the honeycomb lattice. The\nlatter model is known to be the O(n) model at T=0 and corresponds to the\nintegrable model connected to the affine $A_2^{(1)}$ Lie algebra. Thus it is\nshown that the weights of the square-triangle random tiling satisfy the\nYang-Baxter equation, albeit in a singular limit of a more general model. The\nthree colouring model for general vertex weights is solved by algebraic Bethe\nAnsatz.",
"arxiv_id": "solv-int/9611005",
"authors": [
"Jan de Gier",
"Bernard Nienhuis"
],
"categories": [
"solv-int",
"cond-mat.stat-mech",
"nlin.SI"
],
"doi": "10.1103/PhysRevE.55.3926",
"journal_ref": "Phys. Rev. E 55, 3926 (1997)",
"title": "On the integrability of the square-triangle random tiling model",
"url": "https://arxiv.org/abs/solv-int/9611005"
},
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