Delocalization of the height function of the six-vertex model

  • Hugo Duminil-Copin

    Université de Genève, Switzerland; Institut des Hautes Études Scientifiques, Bures-sur-Yvette, France
  • Alex M. Karrila

    Åbo Akademi University, Finland
  • Ioan Manolescu

    Université de Fribourg, Switzerland
  • Mendes Oulamara

    Université Paris-Saclay, Orsay, France; Institut des Hautes Études Scientifiques, Bures-sur-Yvette, France
Delocalization of the height function of the six-vertex model cover
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Abstract

We show that the height function of the six-vertex model, in the parameter range and , is delocalized with logarithmic variance when . This complements the earlier proven localization for . 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.

Cite this article

Hugo Duminil-Copin, Alex M. Karrila, Ioan Manolescu, Mendes Oulamara, Delocalization of the height function of the six-vertex model. J. Eur. Math. Soc. 26 (2024), no. 11, pp. 4131–4190

DOI 10.4171/JEMS/1436