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Many polymers in biological environments such as, e.g., actin filaments, which play an important role for the shape, locomotion, and division of cells, are relatively stiff objects. The stiffness of a polymer is characterized by its persistence length, i.e., by the length on which the chain loses its orientational order. On length scales which are small compared to this persistence length the statistical properties of polymers are dominated by their bending rigidity and the polymers behave as semi-flexible, wormlike chains with an average orientation.
Semi-flexible polymers can appear in bundles where they are bound together by attractive forces. The energy gain from those interactions competes with the loss of entropy of the bound state compared to the state in which the polymers can fluctuate independently of each other. This competition leads to a phase transition, the so called unbinding transition.
Such an unbinding transition also appears for other fluctuating objects. There are for example one-dimensional fluctuating objects the energy of which is given by their line tension instead of their curvature. Those objects are called "strings" or "directed polymers". They can be realized as steps on a vicinal crystal surface, as vortex lines in a type II superconductor or as ordinary flexible polymers in a hydrodynamic flux. But also two-dimensional objects as e.g. interfaces and lipid membranes show unbinding transitions. Even the roughening transition which arises e.g. at a crystal surface growing by molecular beam epitaxy can be understood as an unbinding transition by the Hopf-Cole-transformation and the replica trick.
In order to get a unified picture of all these unbinding transitions in this thesis a renormalization group method is developed that can at least describe the critical behavior of the one-dimensional fluctuating objects at their unbinding transitions. The method is developed in the framework of the simplest such system at hand, which is the system of two strings interacting via a short-range attraction. In this case exact results are known, so that the method can be checked at this system.
Since the method only relies on some quite general conditions it can be directly applied to a system of two semi-flexible polymers. By that means it is possible to give a classification of the unbinding transitions of semi-flexible polymers. The predictions can be confirmed by numerical calculations at this system.
Moreover the method can be extended to a system of many interacting strings. For this system it can be shown that the critical behavior near 4 dimensions does not depend on the number of strings. It can be shown that the well-known mathematical difficulties of this problem near 4 dimensions lead to a non-analytical behavior of a physical quantity. By the connection between this problem and the surface growth problem as it is described by the KPZ-equation in can be concluded that dimension 4 plays a special role in the surface growth problem. This could be a hint in the direction of the discussion about the upper critical dimension of the KPZ Problem.
The whole thesis takes some 1,4MB as a gzipped postscript-file.