dorsal/arxiv
View SchemaExact Solution of an Octagonal Random Tiling Model
| Authors | Jan de Gier, Bernard Nienhuis |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9602002 |
| URL | https://arxiv.org/abs/solv-int/9602002 |
| DOI | 10.1103/PhysRevLett.76.2918 |
| Journal | Phys. Rev. Lett. 76 (1996) 2918-2921 |
Abstract
We consider the two-dimensional random tiling model introduced by Cockayne, i.e. the ensemble of all possible coverings of the plane without gaps or overlaps with squares and various hexagons. At the appropriate relative densities the correlations have eight-fold rotational symmetry. We reformulate the model in terms of a random tiling ensemble with identical rectangles and isosceles triangles. The partition function of this model can be calculated by diagonalizing a transfer matrix using the Bethe Ansatz (BA). The BA equations can be solved providing {\em exact} values of the entropy and elastic constants.
{
"annotation_id": "bd42e460-cd4d-48ae-880d-0e3fa2c63400",
"date_created": "2026-03-02T18:02:51.402000Z",
"date_modified": "2026-03-02T18:02:51.402000Z",
"file_hash": "2cad6c12487c814d6f8656776e62dd4a616ac37604daa62d5a0fa7098a847e64",
"private": false,
"record": {
"abstract": "We consider the two-dimensional random tiling model introduced by Cockayne,\ni.e. the ensemble of all possible coverings of the plane without gaps or\noverlaps with squares and various hexagons. At the appropriate relative\ndensities the correlations have eight-fold rotational symmetry. We reformulate\nthe model in terms of a random tiling ensemble with identical rectangles and\nisosceles triangles. The partition function of this model can be calculated by\ndiagonalizing a transfer matrix using the Bethe Ansatz (BA). The BA equations\ncan be solved providing {\\em exact} values of the entropy and elastic\nconstants.",
"arxiv_id": "solv-int/9602002",
"authors": [
"Jan de Gier",
"Bernard Nienhuis"
],
"categories": [
"solv-int",
"cond-mat",
"hep-th",
"nlin.SI"
],
"doi": "10.1103/PhysRevLett.76.2918",
"journal_ref": "Phys. Rev. Lett. 76 (1996) 2918-2921",
"title": "Exact Solution of an Octagonal Random Tiling Model",
"url": "https://arxiv.org/abs/solv-int/9602002"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "144c3d51-47d0-4d9d-a302-19a942898a54",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}