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On the six-vertex model's free energy

Hugo Duminil-Copin, Karol Kajetan Kozlowski, Dmitry Krachun, Ioan Manolescu, Tatiana Tikhonovskaia

21/12/20 Published in : arXiv:2012.11675

In this paper, we provide new proofs of the existence and the condensation of Bethe roots for the Bethe Ansatz equation associated with the six-vertex model with periodic boundary conditions and an arbitrary density of up arrows (per line) in the regime \Delta<1. As an application, we provide a short, fully rigorous computation of the free energy of the six-vertex model on the torus, as well as an asymptotic expansion of the six-vertex partition functions when the density of up arrows approaches 1/2. This latter result is at the base of a number of recent results, in particular the rigorous proof of continuity/discontinuity of the phase transition of the random-cluster model, the localization/delocalization behaviour of the six-vertex height function when a=b=1 and c\ge1, and the rotational invariance of the six-vertex model and the Fortuin-Kasteleyn percolation.

Entire article

Phase I & II research project(s)

  • Statistical Mechanics

Rotational invariance in critical planar lattice models

Delocalization of the height function of the six-vertex model

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  • Co-leading house


The National Centres of Competence in Research (NCCRs) are a funding scheme of the Swiss National Science Foundation

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