Delocalization of the height function of the six-vertex model

Hugo Duminil-Copin; Alex m. Karrila; Ioan Manolescu; Mendes Oulamara

doi:10.4171/jems/1436

Delocalization of the height function of the six-vertex model

Hugo Duminil-Copin, Alex m. Karrila, Ioan Manolescu, Mendes Oulamara

Mathematics

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Abstract

We show that the height function of the six-vertex model, in the parameter range a D b D 1 and c ≥ 1, is delocalized with logarithmic variance when c ≤ 2. This complements the earlier proven localization for 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.

Original language	English
Pages (from-to)	4131–4190
Journal	Journal of the European Mathematical Society
Volume	26
Issue number	11
DOIs	https://doi.org/10.4171/jems/1436
Publication status	Published - 27 Feb 2024
MoE publication type	A1 Journal article-refereed

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Delocalization of the height function of the six-vertex modelFinal published version, 1.25 MBLicence: CC BY

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abstract = "We show that the height function of the six-vertex model, in the parameter range a D b D 1 and c ≥ 1, is delocalized with logarithmic variance when c ≤ 2. This complements the earlier proven localization for 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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AU - Duminil-Copin, Hugo

AU - Karrila, Alex m.

AU - Manolescu, Ioan

AU - Oulamara, Mendes

PY - 2024/2/27

Y1 - 2024/2/27

N2 - We show that the height function of the six-vertex model, in the parameter range a D b D 1 and c ≥ 1, is delocalized with logarithmic variance when c ≤ 2. This complements the earlier proven localization for 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.

AB - We show that the height function of the six-vertex model, in the parameter range a D b D 1 and c ≥ 1, is delocalized with logarithmic variance when c ≤ 2. This complements the earlier proven localization for 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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Delocalization of the height function of the six-vertex model

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