Exact Solution of the Discrete (1+1)-dimensional RSOS Model with Field and Surface Interactions

TL;DR

This paper provides an exact solution to a linear (1+1)-dimensional RSOS model with field and surface interactions, revealing new mathematical structures involving hypergeometric functions relevant to phase boundaries and non-equilibrium systems.

Contribution

It offers the first exact solution to a restricted SOS model with field, introducing novel hypergeometric function solutions to lattice path problems.

Findings

Solution involves basic hypergeometric functions ${}_3 ext{phi}_2$

Reveals new form of lattice path generating functions

Connects to phase boundary and non-equilibrium models

Abstract

We present the solution of a linear Restricted Solid--on--Solid (RSOS) model in a field. Aside from the origins of this model in the context of describing the phase boundary in a magnet, interest also comes from more recent work on the steady state of non-equilibrium models of molecular motors. While similar to a previously solved (non-restricted) SOS model in its physical behaviour, mathematically the solution is more complex. Involving basic hypergeometric functions ${}_3\phi_2$, it introduces a new form of solution to the lexicon of directed lattice path generating functions.