Typical height of the (2+1)-D Solid-on-Solid surface with pinning above a wall in the delocalized phase

Naomi Feldheim, Shangjie Yang

Research output: Contribution to journalArticlepeer-review

Abstract

We study the typical height of the (2+1)-dimensional solid-on-solid surface with pinning interacting with an impenetrable wall in the delocalization phase. More precisely, let ΛN be a N×N box of Z2, and we consider a nonnegative integer-valued field (ϕ(x))x∈ΛN with zero boundary conditions (i.e. ϕ|ΛN=0) associated with the energy functional V(ϕ)=β∑x∼y|ϕ(x)−ϕ(y)|−∑xh1{ϕ(x)=0}, where β>0 is the inverse temperature and h≥0 is the pinning parameter. Lacoin has shown that for sufficiently large β, there is a phase transition between delocalization and localization at the critical point hw(β)=log [Formula presented]. In this paper we show that for β≥1 and h∈(0,hw), the values of ϕ concentrate at the height H=⌊(4β)−1logN⌋ with constant order fluctuations. Moreover, at criticality h=hw, we provide evidence for the conjectured typical height Hw=⌊(6β)−1logN⌋.

Original languageEnglish
Pages (from-to)168-182
Number of pages15
JournalStochastic Processes and their Applications
Volume165
DOIs
StatePublished - Nov 2023

Bibliographical note

Publisher Copyright:
© 2023 Elsevier B.V.

Keywords

  • Delocalization behavior
  • Random surface
  • Solid-On-Solid
  • Typical height
  • Wetting

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