SURFACE CRITICAL EXPONENTS FOR A 3-DIMENSIONAL MODIFIED SPHERICAL MODEL

A modified three-dimensional mean spherical model with a L-layer dim g eometry under Neumann-Neumann boundary conditions is considered. Two s pherical fields are present in the model: a surface one fixes the mean square value of the spins at the boundaries at some p > 0, and a bulk one imposes the standard spherical constraint (the mean square value of the spins in the bulk equals 1). The surface susceptibility chi(1,1 ) has been evaluated exactly. For p = 1 we find that chi(1,1) is finit e at the bulk critical temperature T-c, in contrast to the recently de rived value of gamma(1,1) = 1 in the case of just one global spherical constraint. The result gamma(1,1) = 1 is only recovered if p = p(c) = 2 - (12K(c))(-1), where K-c is the dimensionless critical coupling. W hen p > p(c), chi(1,1) diverges exponentially as T --> T-c(+). An effe ctive Hamiltonian is also proposed which leads to an exactly solvable model with gamma(1,1) = 2, the value for the n --> infinity limit of t he corresponding O(n) model.