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)

References in corpus (5)

• Theory of a spherical quantum rotors model: low--temperature regime and finite-size scaling
• Exact critical exponent for the shortest-path scaling function in percolation
• Test of renormalization predictions for universal finite-size scaling functions
• Finite-Size Effects in the ${\varphi }^4$ Field Theory Above the Upper Critical Dimension
• Finite size scaling investigations in the quantum ${\varphi }^4$-model with long-range interaction

Cited by in corpus (7)

• Generalized Mittag-Leffler functions in the theory of finite-size scaling for systems with strong anisotropy and/or long-range interaction
• Critical Casimir forces for $\mathcal{O}(n)$ systems with long-range interaction in the spherical limit
• Critical behavior of systems with long-range interaction in restricted geometry
• On the Finite Size Scaling in Disordered Systems
• Thermodynamics from a scaling Hamiltonian
• Scaling behavior for finite O(n) systems with long-range interaction
• Dynamic critical phenomena in disordered systems with finite geometry