Density profiles in the raise and peel model with and without a wall. Physics and combinatorics

TL;DR

This paper studies density profiles in the raise and peel model with an attractive wall, revealing deep connections, unexpected critical exponents, and solutions to recurrence relations related to combinatorial structures.

Contribution

It introduces new combinatorial solutions and explores the impact of walls on density profiles in a fluctuating interface model, linking physics and combinatorics.

Findings

Deep connection between profiles with and without the wall

Unexpected critical exponents discovered

Solutions to new recurrence relations related to alternating sign matrices

Abstract

We consider the raise and peel model of a one-dimensional fluctuating interface in the presence of an attractive wall. The model can also describe a pair annihilation process in a disordered unquenched media with a source at one end of the system. For the stationary states, several density profiles are studied using Monte Carlo simulations. We point out a deep connection between some profiles seen in the presence of the wall and in its absence. Our results are discussed in the context of conformal invariance ($c = 0$ theory). We discover some unexpected values for the critical exponents, which were obtained using combinatorial methods. We have solved known (Pascal's hexagon) and new (split-hexagon) bilinear recurrence relations. The solutions of these equations are interesting on their own since they give information on certain classes of alternating sign matrices.