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

Naomi Feldheim and Shangjie Yang

Stochastic Processes and their Applications, 2023, vol. 165, issue C, 168-182

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)=loge4βe4β−1. 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⌋.

Keywords: Random surface; Solid-On-Solid; Wetting; Typical height; Delocalization behavior (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spa.2023.08.009

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