Delocalization of the height function of the six-vertex model
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2020
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| _version_ | 1866910041811976192 |
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| author | Duminil-Copin, Hugo Karrila, Alex Manolescu, Ioan Oulamara, Mendes |
| author_facet | Duminil-Copin, Hugo Karrila, Alex Manolescu, Ioan Oulamara, Mendes |
| contents | We show that the height function of the six-vertex model, in the parameter range $\mathbf a=\mathbf b=1$ and $\mathbf c\ge1$, is delocalized with logarithmic variance when $\mathbf c\le 2$. This complements the earlier proven localization for $\mathbf c>2$. Our proof relies on Russo--Seymour--Welsh type arguments, and on the local behaviour of the free energy of the cylindrical six-vertex model, as a function of the unbalance between the number of up and down arrows. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2012_13750 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Delocalization of the height function of the six-vertex model Duminil-Copin, Hugo Karrila, Alex Manolescu, Ioan Oulamara, Mendes Probability Mathematical Physics 60K35, 82B20, 82B27 We show that the height function of the six-vertex model, in the parameter range $\mathbf a=\mathbf b=1$ and $\mathbf c\ge1$, is delocalized with logarithmic variance when $\mathbf c\le 2$. This complements the earlier proven localization for $\mathbf c>2$. Our proof relies on Russo--Seymour--Welsh type arguments, and on the local behaviour of the free energy of the cylindrical six-vertex model, as a function of the unbalance between the number of up and down arrows. |
| title | Delocalization of the height function of the six-vertex model |
| topic | Probability Mathematical Physics 60K35, 82B20, 82B27 |
| url | https://arxiv.org/abs/2012.13750 |