Lattice gas generalization of the hard hexagon model. I. Star-triangle relation and local densities
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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 mostn particles per pair of adjacent sites: this involves all Gordon's relations, as well as others that we will discuss in a subsequent paper.
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- Lattice gas generalization of the hard hexagon model. I. Star-triangle relation and local densities
Journal of Statistical Physics
Volume 44, Issue 1-2 , pp 249-271
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers-Plenum Publishers
- Additional Links
- Statictical mechanics
- lattice gas
- star-triangle relation
- Yang-Baxter relation
- Industry Sectors
- Author Affiliations
- 1. Research School of Physical Sciences, The Australian National University, G.P.O. Box 4, 2601, Canberra, Australia
- 2. Department of Mathematics, McAllister Building, Pennsylvania State University, 16802, University Park, Pennsylvania, USA