2 research outputs found
Generalized Mittag-Leffler functions in the theory of finite-size scaling for systems with strong anisotropy and/or long-range interaction
The difficulties arising in the investigation of finite-size scaling in
--dimensional O(n) systems with strong anisotropy and/or long-range
interaction, decaying with the interparticle distance as
(), are discussed. Some integral representations aiming at the
simplification of the investigations are presented for the classical and
quantum lattice sums that take place in the theory. Special attention is paid
to a more general form allowing to treat both cases on an equal footing and in
addition cases with strong anisotropic interactions and different geometries.
The analysis is simplified further by expressing this general form in terms of
a generalization of the Mittag-Leffler special functions. This turned out to be
very useful for the extraction of asymptotic finite-size behaviours of the
thermodynamic functions.Comment: Accepted for publication in J. Phys. A: Math. and Gen.; 14 pages. The
manuscript has been improved to help reader
Exact results for some Madelung type constants in the finite-size scaling theory
A general formula is obtained from which the madelung type constant: extensively used in the finite-size
scaling theory is computed analytically for some particular cases of the
parameters and . By adjusting these parameters one can obtain
different physical situations corresponding to different geometries and
magnitudes of the interparticle interaction.Comment: IOP- macros, 5 pages, replaced with amended version (1 ref. added