On the finite-size scalling equation for the spherical model

The mean spherical model with an arbitrary interaction potential, the Fourier transform of which has a long-wavelength exponent σ, 0 < σ ≤ 2, is considered under periodic boundary conditions and fully finite geometry in d dimensions, when σ < d < 2σ. A new form of the finite-size scaling equation for the spherical field in the critical region is derived, which relates the temperature shift to Madelung-type lattice constants. The method of derivation makes use of the Poisson summation formula and a Laplace transformation of the momentum-space correlation function