Delocalization transitions of low-dimensional manifolds

Abstract

The behavior of low-dimensional manifolds such as interfaces, membranes, or polymers in an external potential is studied in d=${\mathit{d}}_{\mathrm{\parallel }}$+${\mathit{d}}_{\mathrm{\perp }}$ dimensions. If the potential has several minima, the manifolds can undergo nontrivial transitions from a localized to a delocalized state at a characteristic temperature T=${\mathit{T}}_{\mathrm{*}}$. For interfaces in d=1+1, several universality classes must be distinguished which can be determined exactly by transfer-matrix methods. The same classification also applies to (self-intersecting) polymers in d=1+${\mathit{d}}_{\mathrm{\perp }}$. Within a functional renormalization-group approach, the critical behavior is governed by a line of fixed points in close analogy with unbinding transitions. However, in contrast to unbinding, this fixed point line now contains the trivial fixed point at which one can determine the spectrum of eigenperturbations exactly. The number of relevant eigenperturbations increases monotonically with the decay exponent τ=${\mathit{d}}_{\mathrm{\parallel }}$/ζ where the roughness exponent ζ characterizes the delocalized manifold.