Book/Report

FZJ-2018-03161

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Funktionale Renormierung an einem Modell zum Benetzungsübergang

Jülicher, F. (Corresponding author)FZJ*

1989
Kernforschungsanlage Jülich, Verlag Jülich

Please use a persistent id in citations: http://hdl.handle.net/2128/18679

Report No.: Juel-2318

Abstract: In this work, we use effective interface models in low dimensions to study wetting transitions of a fluctuating interface at a hard wall in long- and short ranged interaction potentials. The starting point are models in $\textit{d}$ = 1 + 1 dimensions, which we study using transfermatrix- and renormalization group methods. The renormalization group can be generalized to arbitrary dimensions $\textit{d}$. The structure of wetting transitions which we find for the SOS-model with special interaction potentials is shown to be the same as recent results obtained with an continuum model (Schrödinger equation). Starting with the Gaussian model, we define an $\textit{exact functional renormalization group}$ (RG) in $\textit{d}$ = 1 + 1. This RG shows, that the critical behaviour at these wetting transitions is in fact $\textit{universal}$ for the different models. Our exact RG has the following properties: (i) it acts in the function space of potentials, U(z, z'), where z and z' represent the separation of the interface and the wall; (ii) it has a line of fixed points, U* (z, z'). These fixed points exhibit an unexpected symmetry since they depend only on the product z $\cdot$ z': U * (z, z' ) = $\overline{U}$(z $\cdot$ z'); (iii) the line of fixed points exhibits two branches, and the RG flow has a parabolic character describing two subregimes (A) and (B). (iv) In addition, the RG flow leads to a separatrix which represents an analytic continuation of the fixed point line. This separatrix belongs to a third subregime (C) where the wetting transitions are first-order but have unusual scaling properties. As one approaches the boundary between the line of fixed points and this separatrix, the fixed points on the two branches are found to be identical apart from a singular piece at z $\cdot$ z' = 0. In this way, the line of :faxed points contains a $\textit{closed loop}$ in function space. The decimation-type RG can be generalized to wetting in $\textit{d}$ $\neq$ 1 + 1 via a Migdal-Kadanoff bond moving scheme. This generalized scheme (which is no longer exact) indicates that the presence of subregime (C) might be a specialfeature of wetting in $\textit{d}$ = 1 + 1.

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Contributing Institute(s):

1. Publikationen vor 2000 (PRE-2000)

Research Program(s):

1. 899 - ohne Topic (POF3-899) (POF3-899)

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