Critical behaviour of the spherical model with enhanced surface exchange: two spherical fields

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Abstract
The local surface susceptibility chi 1,1(T) is calculated and analysed in detail for a ferromagnetic spherical model on a d-dimensional hypercubic half-space bounded by a free surface in which the exchange coupling, J(1+ Delta ) with Delta >0, is enhanced over the bulk value J. A separate spherical field for the free surfaces is introduced to ensure the proper behaviour of surface spins. In contrast with previous results and the results of the mean-field approximation, it is found that chi 1,1(T) is non-singular at all temperatures above the critical temperature when d<or=3.