Abstract
The phase transition of a manifold from a state bound to a surface to an unbound state is considered. The manifold feels an effective external potential which is motivated by the respective physical system. A general classification transition is presented. Within this scheme the phase transition depends on the external potential and on the lateral dimension of the manifold. Two classes of potentials were investigated. Potentials of the first class contain a hard wall. This hard wall prevents the use of perturbation or linearization methods. However, the approximate renormalization group is nonlinear and the conditions of a hard wall can be considered. It turns out that the limit d {yields} 3 for interfaces is nonanalytic, since the renormalization group has no fixed points at d = 3 anymore where d = 3 is just the dimension in which the interface is marginal i.e. logarithmically rough. In d > 3 one expects mean field behaviour of the phase transition. In contrast to bulk critical phenomena one finds a nonanalytic behaviour of the renormalization group when the upper critical dimension is reached. This shows up in a complex bifurcation structure of the fixed points. This limit is studied in detail for wetting
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Citation Formats
Grotehans, S.
Critical behavior of interfaces and membranes; Kritisches Verhalten von Grenzflaechen und Membranen.
Germany: N. p.,
1992.
Web.
Grotehans, S.
Critical behavior of interfaces and membranes; Kritisches Verhalten von Grenzflaechen und Membranen.
Germany.
Grotehans, S.
1992.
"Critical behavior of interfaces and membranes; Kritisches Verhalten von Grenzflaechen und Membranen."
Germany.
@misc{etde_10148239,
title = {Critical behavior of interfaces and membranes; Kritisches Verhalten von Grenzflaechen und Membranen}
author = {Grotehans, S}
abstractNote = {The phase transition of a manifold from a state bound to a surface to an unbound state is considered. The manifold feels an effective external potential which is motivated by the respective physical system. A general classification transition is presented. Within this scheme the phase transition depends on the external potential and on the lateral dimension of the manifold. Two classes of potentials were investigated. Potentials of the first class contain a hard wall. This hard wall prevents the use of perturbation or linearization methods. However, the approximate renormalization group is nonlinear and the conditions of a hard wall can be considered. It turns out that the limit d {yields} 3 for interfaces is nonanalytic, since the renormalization group has no fixed points at d = 3 anymore where d = 3 is just the dimension in which the interface is marginal i.e. logarithmically rough. In d > 3 one expects mean field behaviour of the phase transition. In contrast to bulk critical phenomena one finds a nonanalytic behaviour of the renormalization group when the upper critical dimension is reached. This shows up in a complex bifurcation structure of the fixed points. This limit is studied in detail for wetting and adhesion phenomena. Symmetrical potentials are the second class which are considered. The order of the phase transition for this class is also investigated. Motivated by the calculations for potentials with a hard wall the limit d {yields} 3 is again studied. (orig./GSCH).}
place = {Germany}
year = {1992}
month = {Sep}
}
title = {Critical behavior of interfaces and membranes; Kritisches Verhalten von Grenzflaechen und Membranen}
author = {Grotehans, S}
abstractNote = {The phase transition of a manifold from a state bound to a surface to an unbound state is considered. The manifold feels an effective external potential which is motivated by the respective physical system. A general classification transition is presented. Within this scheme the phase transition depends on the external potential and on the lateral dimension of the manifold. Two classes of potentials were investigated. Potentials of the first class contain a hard wall. This hard wall prevents the use of perturbation or linearization methods. However, the approximate renormalization group is nonlinear and the conditions of a hard wall can be considered. It turns out that the limit d {yields} 3 for interfaces is nonanalytic, since the renormalization group has no fixed points at d = 3 anymore where d = 3 is just the dimension in which the interface is marginal i.e. logarithmically rough. In d > 3 one expects mean field behaviour of the phase transition. In contrast to bulk critical phenomena one finds a nonanalytic behaviour of the renormalization group when the upper critical dimension is reached. This shows up in a complex bifurcation structure of the fixed points. This limit is studied in detail for wetting and adhesion phenomena. Symmetrical potentials are the second class which are considered. The order of the phase transition for this class is also investigated. Motivated by the calculations for potentials with a hard wall the limit d {yields} 3 is again studied. (orig./GSCH).}
place = {Germany}
year = {1992}
month = {Sep}
}