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

H. Chamati·N. S. Tonchev
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Abstract

A general formula is obtained from which the madelung type constant: $$ C(d|ν)=\int_0^\infty dx x^{d/2-ν-1}[(\sum_{l=-\infty}^\infty e^{-xl^2})^d-1-(\fracπx)^{d/2}] $$ extensively used in the finite-size scaling theory is computed analytically for some particular cases of the parameters $d$ and $ν$. By adjusting these parameters one can obtain different physical situations corresponding to different geometries and magnitudes of the interparticle interaction.

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H. Chamati, N. S. Tonchev. 2000-05-12. Exact results for some Madelung type constants in the finite-size scaling theory. https://doi.org/10.1088/0305-4470%2F33%2F19%2F101

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