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

2025/05/22 by Sébastien Ott, Ott, Sébastien, Florian Schweiger +1
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2505.16804

openalex publication_date 2025/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a family of integer-valued random interface models on the two-dimensional square lattice that include the solid-on-solid model and more generally p-SOS models for 0

Citations

• Invisibility of the integers for the discrete Gaussian chain via a Caffarelli-Silvestre extension of the discrete fractional Laplacian
• On the duality between height functions and continuous spin models
• Depinning in integer-restricted Gaussian Fields and BKT phases of two-component spin models
• Delocalization of the height function of the six-vertex model
• Maximum of the integer-valued Gaussian free field

Related

• Stability for a continuous SOS-interface model in a randomly perturbed periodic potential
• Critical wetting in the (2+1)D Solid-On-Solid model
• Rigidity of the interface for percolation and random-cluster models
• Logarithmic delocalization of low temperature 3D Ising and Potts interfaces above a hard floor
• Long range order in atomistic models for solids