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 studied by the example of the mean spherical model. The general case of a hypercubic lattice of arbitrary dimensionality d > 2, under boundary conditions which are periodic in d' greater-than-or-equal-to 0 dimensions and free in the remaining d - d' dimensions is considered. The critical 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-logarithmic corrections due to corners and logarithmic corrections due to one-dimensional edges in the regime L/xi(L) is-proportional-to ln L which takes place at the bulk critical point.