Analytic Solution of Emden-Fowler Equation and Critical Adsorption in Spherical Geometry

Details Analytic Solution of Emden-Fowler Equation and Critical Adsorption in Spherical Geometry Analytic Solution of Emden-Fowler Equation and Critical Adsorption in Spherical Geometry

1994-09-14

arxiv.org/abs/cond-mat/9409059v1

Z. Phys. B 96 (1995) 391

Physics

Condensed Matter

(to be published in Z. Phys. B), 7 pages, 1 figure, uuencoded postscript file, 8-94

Scientific paper

10.1007/BF01313061

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 $d=4$ 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.

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