Archimedean Ice
The striking boundary dependency (the Arctic Circle phenomenon) exhibited in the ice model on the square lattice extends to other planar set-ups. We present these findings for the triangular and the Kagome lattices. Critical connectivity results guarantee that ice configurations can be generated usi...
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| Format: | Report |
| Language: | unknown |
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arXiv
2009
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| Online Access: | https://dx.doi.org/10.48550/arxiv.0909.4007 https://arxiv.org/abs/0909.4007 |
| Summary: | The striking boundary dependency (the Arctic Circle phenomenon) exhibited in the ice model on the square lattice extends to other planar set-ups. We present these findings for the triangular and the Kagome lattices. Critical connectivity results guarantee that ice configurations can be generated using the simplest and most efficient local actions. Height functions are utilized throughout the analysis. At the end there is a surprise in store: on the remaining Archimedean lattice for which the ice model can be defined, the 3.4.6.4. lattice, the long range behavior is completely different from the other cases. : 20 pages, 6 figures (last page pics may take a bit time to upload) |
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