# The exact solution of the (1+1)-dimensional Restricted Solid-on-Solid model in a field: A new type of lattice path generating function or Why simpler isn't always easier

#### by Aleks Owczarek

Institution: The University of Melbourne, Department of Mathematics and Statistics
Date: Mon 10th August 2009
Time: 1:00 PM
Location: Old Geology Theatre 2

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.