The interface
between two media may wander, which leads to non-trivial statistical properties.
An interface in a plane can be seen as a (directed) polymer.
Studied problems involve an interface in d=2 in the presence of a disordered
substate [L6], [P21], first order depinning transitions [P22], [L8], an intermediate
fluctuation regime [L9], and a nice problem of polymer adsorption in the presence
of disorder [L14].
A review about this subject was written, [R1].
[R1] G. Forgacs, R. Lipowsky and Th.M. N., The behavior of interfaces in
ordered and in disordered systems, In ``Phase Transitions and Critical
Phenomena 14'', C. Domb and J. Lebowitz, eds. (Academic, New York, 1991) pp
135-363
[L14] Th.M.
N. and G. Forgacs, Polymer adsorption in a random environment,
Europhys. Lett. 15 (1991) 837-842
[L9] Th.M.
N., Disorder-induced first-order wetting transitions in two dimensions,
J. Phys. A Lett.
21 (1988) L567-L571
[L8] R. Lipowsky and Th.M. N., Intermediate fluctuation regime for wetting transitions in two dimensions, J. Phys. A Lett. 21 (1988) L89-L94
[L6] G. Forgacs, J.M. Luck, Th.M. N., and H. Orland, Wetting of a disordered substrate: Exact critical behavior in two dimensions, Phys. Rev. Lett. 57 (1986) 2184-2187
[P22] G.
Forgacs and Th.M. N., Disorder driven crossover from first-order to second-order
depinning,
J. Phys. A 21 (1988) 3871-3876
[P21] G. Forgacs, J.M. Luck, Th.M. N., and H. Orland, Exact crical behavior of two-dimensional wetting problems, J. Stat. Phys. 51 (1988) 29-56