EXACT 3-DIMENSIONAL CASIMIR FORCE AMPLITUDE, C-FUNCTION, AND BINDER CUMULANT RATIO - SPHERICAL MODEL RESULTS

The three-dimensional mean spherical model on a hypercubic lattice wit h a film geometry L x infinity(2) under periodic boundary conditions i s considered in the presence of an external magnetic field H. The univ ersal Casimir amplitude Delta and the Binder's cumulant ratio B are ca lculated exactly and found to be Delta = - 2 zeta(3)/(5 pi) approximat e to - 0.153051 and B = 2 pi/{root 51n(3)[(1 + root 5)/2]}. A discussi on on the relations between the finite temperature C function, usually defined for quantum systems, and the excess free energy (due to the f inite-size contributions to the free energy of the system) scaling fun ction is presented. It is demonstrated that the C function of the mode l equals 4/5 at the bulk critical temperature T-c. It is analytically shown that the excess free energy is a monotonically increasing functi on of the temperature T and of the magnetic field \H\ in the vicinity of T-c. This property is supposed to hold for any classical d-dimensio nal O(n),n>2, model with a film geometry under periodic boundary condi tions when d less than or equal to 3. An analytical evidence is also p resented to confirm that the Casimir force in the system is negative b oth below and in the vicinity of the bulk critical temperature T-c.