Exact Solution of the Discrete (1+1)-dimensional RSOS Model in a Slit with Field and Wall Interactions
arXiv:1004.1698 · doi:10.1088/1751-8113/43/37/375004
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 and including an osmotic pressure. This work generalises 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 . Because of the mathematical relationship between half-plane and slit this work hence effectively explores the underlying -orthogonal polynomial structure to that solution. It also generalises 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.