Surface magnetisation profile in the critical region by the epsilon -expansion

The Wilson perturbation theory technique is used to investigate the spontaneous magnetisation profile in the critical region for the ordinary transition of a scalar (n=1) semi-infinite model. The behaviour in the vicinity of the surface is explicitly determined and the surface exponent beta 1 identified to be 1- epsilon /6 to first order in epsilon =4-d, in agreement with the scaling prediction of Bray and Moore (1977).