Exact results for some Madelung type constants in the finite-size scaling theory

Abstract

A general formula is obtained from which the madelung type constant: $$C(d|\nu )={\int }_0^{\infty }dx{x}^{d/2-\nu -1}[(\sum _{l=-\infty }^{\infty }{e}^{-x{l}^2}{)}^d-1-(\frac{\pi }{x}{)}^{d/2}]$$ extensively used in the finite-size scaling theory is computed analytically for some particular cases of the parameters $d$ and $\nu$. By adjusting these parameters one can obtain different physical situations corresponding to different geometries and magnitudes of the interparticle interaction.

IOP- macros, 5 pages, replaced with amended version (1 ref. added)