FINITE-SIZE LOGARITHMIC CORRECTIONS IN THE FREE-ENERGY OF THE MEAN SPHERICAL MODEL

The validity of the finite-size scaling prediction about the existence of logarithmic mic corrections in the free energy due to corners is s tudied by the example of the mean spherical model. The general case of a hypercubic lattice of arbitrary dimensionality d > 2, under boundar y conditions which are periodic in d' greater-than-or-equal-to 0 dimen sions and free in the remaining d - d' dimensions is considered. The c ritical regime, as the size of the system L --> infinity, is specified by the asymptotic behaviour of the ratio L/xi(L), where xi(L) is the correlation length of the finite system. New results are the double-lo garithmic corrections due to corners and logarithmic corrections due t o one-dimensional edges in the regime L/xi(L) is-proportional-to ln L which takes place at the bulk critical point.