Exact solution of the discrete (1+1)-dimensional RSOS model in a slit with field and wall interactions

Abstract

We present the solution of a linear restricted solid-on-solid (RSOS) model confined to a slit. We include a field-like energy, which equivalently weights the area under the interface, and also include independent interaction terms with both walls. This model can also be mapped to a lattice polymer model of Motzkin paths in a slit interacting with both walls including an osmotic pressure. This work generalizes the previous work on the RSOS model in the half-plane which has a solution that was shown recently to exhibit a novel mathematical structure involving basic hypergeometric functions 3ϕ2. Because of the mathematical relationship between the half-plane and slit this work hence effectively explores the underlying q-orthogonal polynomial structure to that solution. It also generalizes two other recent works: one on Dyck paths weighted with an osmotic pressure in a slit and another concerning Motzkin paths without an osmotic pressure term in a slit.