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

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

2000-03-14

arxiv.org/abs/cond-mat/0003235v2

J. Phys. A:Math. Gen. 33, L167 (2000)

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

10.1088/0305-4470/33/19/101

A general formula is obtained from which the madelung type constant: $$ C(d|\nu)=\int_0^\infty dx x^{d/2-\nu-1}[(\sum_{l=-\infty}^\infty e^{-xl^2})^d-1-(\frac\pi x)^{d/2}] $$ 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.

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