Delocalization of the height function of the six-vertex model

2020/12/26 by Hugo Duminil‐Copin, Duminil-Copin, Hugo, Alex Karrila +5 · 1 citation
Mathematics · Physics and Astronomy · #60K35 #82B20 #82B27 #Benford’s Law and Fraud Detection #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Theoretical and Computational Physics

paper · doi:10.48550/arxiv.2012.13750

openalex publication_date 2020/12/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the height function of the six-vertex model, in the parameter range \mathbf a=\mathbf b=1 and \mathbf c≥1, is delocalized with logarithmic variance when \mathbf c≤ 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.

Cited by

• Quantitative delocalization for solid-on-solid models at high temperature and arbitrary tilt

Related

• Lower tail large deviations of the stochastic six vertex model
• On the six-vertex model's free energy
• A central limit theorem for square ice
• From logarithmic delocalization of the six-vertex height function under sloped boundary conditions to weakened crossing probability estimates for the Ashkin-Teller, generalized random-cluster, and (q_σ,q_τ)-cubic models
• On the duality between height functions and continuous spin models