### Abstract

In the solvable hard hexagon model there is at most one particle in every pair of adjacent sites, and the solution automatically leads to various mathematical identities, in particular to the Rogers-Ramanujan relations. These relations have been generalized by Gordon. Here we construct a solvable model with at most two particles per pair of adjacent sites, and find the solution involves the next of Gordon's relations. We conjecture the corresponding solution for a model with at most n particles per pair of adjacent sites: this involves all Gordon's relations, as well as others that we will discuss in a subsequent paper.

Original language | English (US) |
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Pages (from-to) | 249-271 |

Number of pages | 23 |

Journal | Journal of Statistical Physics |

Volume | 44 |

Issue number | 1-2 |

DOIs | |

State | Published - Jul 1 1986 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

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*Journal of Statistical Physics*, vol. 44, no. 1-2, pp. 249-271. https://doi.org/10.1007/BF01010916

**Lattice gas generalization of the hard hexagon model. I. Star-triangle relation and local densities.** / Baxter, R. J.; Andrews, George E.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Lattice gas generalization of the hard hexagon model. I. Star-triangle relation and local densities

AU - Baxter, R. J.

AU - Andrews, George E.

PY - 1986/7/1

Y1 - 1986/7/1

N2 - In the solvable hard hexagon model there is at most one particle in every pair of adjacent sites, and the solution automatically leads to various mathematical identities, in particular to the Rogers-Ramanujan relations. These relations have been generalized by Gordon. Here we construct a solvable model with at most two particles per pair of adjacent sites, and find the solution involves the next of Gordon's relations. We conjecture the corresponding solution for a model with at most n particles per pair of adjacent sites: this involves all Gordon's relations, as well as others that we will discuss in a subsequent paper.

AB - In the solvable hard hexagon model there is at most one particle in every pair of adjacent sites, and the solution automatically leads to various mathematical identities, in particular to the Rogers-Ramanujan relations. These relations have been generalized by Gordon. Here we construct a solvable model with at most two particles per pair of adjacent sites, and find the solution involves the next of Gordon's relations. We conjecture the corresponding solution for a model with at most n particles per pair of adjacent sites: this involves all Gordon's relations, as well as others that we will discuss in a subsequent paper.

UR - http://www.scopus.com/inward/record.url?scp=34250127795&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34250127795&partnerID=8YFLogxK

U2 - 10.1007/BF01010916

DO - 10.1007/BF01010916

M3 - Article

AN - SCOPUS:34250127795

VL - 44

SP - 249

EP - 271

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 1-2

ER -