Finite-size effects in the spherical model of ferromagnetism: Zero-field susceptibility under antiperiodic boundary conditions

The overall zero-field susceptibility χ¯ of a finite-sized spherical model of spins under various antiperiodic boundary conditions is reexamined with a view to explaining the finite-size effects of an algebraic nature found recently by Singh and Pathria. The cause of this ‘‘unexpected’’ behavior at temperatures above the bulk critical temperature $T_c$(∞) is seen to lie in the spatial variation of the local susceptibility which, on averaging over the system, leads precisely to the effects found previously. Below $T_c$(∞), the influence of antiperiodic conditions is even more severe, in that not only are the finite-size amplitudes for χ¯ modified but, for the local susceptibility, new exponents also appear.