ANALYTIC SOLUTION OF EMDEN-FOWLER EQUATION AND CRITICAL ADSORPTION IN SPHERICAL GEOMETRY

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 Fisherde Gennes effect in the limit of the parallel-plate geometry.