Eur. Phys. J. B 64, 231-235 (2008)
https://doi.org/10.1140/epjb/e2008-00288-4

Indirect magnetic interaction in the “net fractal” systems

Institute of Physics, Jan Dlugosz University of Czestochowa, 42-200 Czestochowa, al. Armii Krajowej 13/15, Poland

Corresponding author: ^a z.bak@ajd.czest.pl

Received: 18 January 2008
Revised: 20 May 2008
Published online: 18 July 2008

Abstract

A localized spin system of fractal symmetry with indirect exchange between them is considered. We define a specific class of fractals as the “net fractals” which display multidimensional logarithmic periodicity. Basing on this property we model the effective indirect exchange interaction by the conventional RKKY exchange with the logarithmic coordinates playing role of the real space ones. Finally, we discuss the case of non-ideal “net fractals” in which fractional dynamics of the electrons is expected. In this case we show that RKKY exchange integrals are given by the formulas derived under assumption that a system has a fractional spectral dimension.