Third-order phase transition in random tilings
We consider the domino tilings of an Aztec diamond with a cut-off corner of macroscopic square shape and given size, and address the bulk properties of tilings as the size is varied. We observe that the free energy exhibits a third-order phase transition when the cut-off square, increasing in size,...
| Main Authors: | , |
|---|---|
| Format: | Text |
| Language: | unknown |
| Published: |
arXiv
2013
|
| Subjects: | |
| Online Access: | https://dx.doi.org/10.48550/arxiv.1306.6207 https://arxiv.org/abs/1306.6207 |
| Summary: | We consider the domino tilings of an Aztec diamond with a cut-off corner of macroscopic square shape and given size, and address the bulk properties of tilings as the size is varied. We observe that the free energy exhibits a third-order phase transition when the cut-off square, increasing in size, reaches the arctic ellipse---the phase separation curve of the original (unmodified) Aztec diamond. We obtain this result by studying the thermodynamic limit of certain nonlocal correlation function of the underlying six-vertex model with domain wall boundary conditions, the so-called emptiness formation probability (EFP). We consider EFP in two different representations: as a tau-function for Toda chains and as a random matrix model integral. The latter has a discrete measure and a linear potential with hard walls; the observed phase transition shares properties with both Gross-Witten-Wadia and Douglas-Kazakov phase transitions. : 21 pages, 6 figures; v3: journal version with misprints in text and Fig. 3 corrected; footnote added at page 3 |
|---|