The Arctic Circle Revisited
The problem of limit shapes in the six-vertex model with domain wall boundary conditions is addressed by considering a specially tailored bulk correlation function, the emptiness formation probability. A closed expression of this correlation function is given, both in terms of certain determinant an...
| Main Authors: | , |
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| Format: | Text |
| Language: | unknown |
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arXiv
2007
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| Subjects: | |
| Online Access: | https://dx.doi.org/10.48550/arxiv.0704.0362 https://arxiv.org/abs/0704.0362 |
| Summary: | The problem of limit shapes in the six-vertex model with domain wall boundary conditions is addressed by considering a specially tailored bulk correlation function, the emptiness formation probability. A closed expression of this correlation function is given, both in terms of certain determinant and multiple integral, which allows for a systematic treatment of the limit shapes of the model for full range of values of vertex weights. Specifically, we show that for vertex weights corresponding to the free-fermion line on the phase diagram, the emptiness formation probability is related to a one-matrix model with a triple logarithmic singularity, or Triple Penner model. The saddle-point analysis of this model leads to the Arctic Circle Theorem, and its generalization to the Arctic Ellipses, known previously from domino tilings. : 16 pages, 3 figures |
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