
Condensed and soft matter systems often contain thin structures such as
(i) domain boundaries, vortex lines,
polymers, and filaments, or (ii) interfaces, monolayers, and membranes etc which behave as
1dimensional lines or 2dimensional surfaces. These
lowdimensional manifolds undergo thermally excited shape fluctuations
in order to increase their configurational entropy. These fluctuations are scaleinvariant
and can be characterized by a corresponding critical exponent.
[1]
[2]
One particularly interesting case are domain boundaries and interfaces in
quasiperiodic systems.

Because of their molecular architecture, 1dimensional lines and 2dimensional surfaces
interact via electrostatic and van der Waals forces or other constraints.
The shape fluctuations renormalize
these latter interactions and lead to
unbinding transitions
between bound and unbound states of the manifolds.
[3]
These latter transitions represent wetting
[4],
adhesion
[5],
and adsorption transitions
[6]
for interfaces, membranes, and polymers, respectively.

In all cases, one encounters a strong fluctuation regime
[7]
with universal
critical behavior
[8]
[9]
as well as an
intermediate fluctuation regime
with more complex behavior
[10]
[11].
In the latter regime, the unbinding transitions are discontinuous and
characterized by a
kink in the internal energy but the shape fluctuations exhibit unusual
properties and are
governed by a power law distribution
[12].

The scaling properties of different systems are found to be related in unexpected ways.
The continuous unbinding of two membranes in three dimensions
[5], for example,
exhibits the same scaling properties as the unbinding of two domain boundaries or "strings"
in two dimensions
[13].
For 1dimensional lines, there is even an intimate relationship between the
scaling properties of bound and unbound states
[14].
Both bundles of N strings in two dimensions
[15]
[16]
and
bunches of N membranes in three dimensions
[17]
undergo continuous unbinding transitions
whereas bundles of N filaments unbind discontinuously in
three dimensions
[18].
In the continuous case, extensive numerical studies
[15]
[17]
and analytical solutions based on a Bethe Ansatz
[16]
have led to somewhat different conclusions about the Ndependence
of the critical exponents which remains an open issue
[19].

Recent studies have focused on the critical behavior of filaments and semiflexible polymers:
 For more information, see
publications
on lines and surfaces.

