Analytic Solution of Emden-Fowler Equation and Critical Adsorption in Spherical Geometry
Condensed Matter
2009-10-22 v1
Abstract
In the framework of mean-field theory the equation for the order-parameter profile in a spherically-symmetric geometry at the bulk critical point reduces to an Emden-Fowler problem. We obtain analytic solutions for the surface universality class of extraordinary transitions in for a spherical shell, which may serve as a starting point for a pertubative calculation. It is demonstrated that the solution correctly reproduces the Fisher-de Gennes effect in the limit of the parallel-plate geometry.
Keywords
Cite
@article{arxiv.cond-mat/9409059,
title = {Analytic Solution of Emden-Fowler Equation and Critical Adsorption in Spherical Geometry},
author = {S. Gnutzmann and U. Ritschel},
journal= {arXiv preprint arXiv:cond-mat/9409059},
year = {2009}
}
Comments
(to be published in Z. Phys. B), 7 pages, 1 figure, uuencoded postscript file, 8-94