Probing Phase Transitions of Finite Directed Polymers near a Corrugated Wall via Two-Replica Analysis
Year: 2026
Type: article
Abstract: We study the pinning transition in a (1+1)-dimensional lattice model of a fluctuating interface interacting with a corrugated impenetrable wall. The interface is modeled as an N-step directed one-dimensional random walk on the half-line x≥0. Its interaction with the wall is described by a quenched, site-dependent, short-ranged random potential uj (j=1,…,N), distributed according to Q(uj) and localized at x=0. By computing the first two disorder-averaged moments of the partition function, ⟨GN⟩ and ⟨GN2⟩, and by analyzing the analytic structure of the resulting expressions, we derive an explicit criterion for the coincidence or distinction of the pinning transitions in annealed and quenched systems. We show that, although the transition points of the annealed and quenched systems are always different in the thermodynamic limit, for finite systems there exists a “gray zone” in which this difference is hardly detectable. Our results may help reconcile conflicting views on whether quenched disorder is marginally relevant.
Source: Entropy
DOI: 10.3390/e28020190
Authors: Ruijie Xu, Sergei Nechaev
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W7128422800