Wetting Transitions for a Random Line in Long-Range Potential

Abstract

We consider a restricted Solid-on-Solid interface in (Formula presented.)Z+, subject to a potential V(n) behaving at infinity like -w/n2. Whenever there is a wetting transition as (Formula presented.) is varied, we prove the following results for the density of returns m(b0) to the origin: if (Formula presented.), then (Formula presented.) has a jump at (Formula presented.) (Formula presented.), then (Formula presented.)where (Formula presented.), there is no wetting transition.