CRITICAL WETTING FOR A RANDOM LINE IN LONG-RANGE POTENTIAL
Résumé
We consider a restricted Solid-on-Solid interface in Z_+, subject to apotential V(n) behaving at infinity like -w/n^2. Whenever there is a wetting transition as b_0=exp V(0) is varied, we prove the following results for the density of returns m(b_0) to the origin: If w<-3/8, then m(b_0) has a jump at b_0^c; if -3/8 < w <1/8, then m(b_0)~(b_0^c-b_0) ^{theta/(1-theta)} where theta=1-sqrt(1-8w)/2. If w >1/8, there is no wetting transition.
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