FINITE-SIZE-SCALING IN THE PRESENCE OF AN INHOMOGENEOUS EXTERNAL-FIELD - AN ANALYTICAL-MODEL TREATMENT

The validity of finite-size scaling in the presence of an inhomogeneou s external field vanishing in the thermodynamic-limit is studied using a fully finite three-dimensional mean spherical model. The external f ield is chosen to change sign stepwise in one space dimension and to b e translationally invariant in the other two dimensions, in which the lattice is assumed periodic. The boundary conditions in the direction of broken translational invariance are (i) periodic, and (ii) free, an d (iii) fixed. Exact expressions for the magnetization profile are der ived and studied. An extended, coordinate-dependent finite-size scalin g is found to hold near the shifted critical temperature. Different sc aling forms hold near the bulk critical temperature: in case (ii) the distance from the boundary scales with the finite-size correlation len gth, and in case (iii) with the linear size of the system.