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arXiv · 2012.13750

Delocalization of the height function of the six-vertex model

Hugo Duminil-Copin·Alex Karrila·Ioan Manolescu·Mendes Oulamara
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Abstract

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.

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Hugo Duminil-Copin, Alex Karrila, Ioan Manolescu, Mendes Oulamara. 2020-12-26. Delocalization of the height function of the six-vertex model. https://doi.org/10.4171/jems/1436

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