2005/10/31 by H. Chamati, H Chamati, N. S. Tonchev +1
Mathematics · Physics and Astronomy · #Nonlinear Photonic Systems #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1088/0305-4470/39/3/001
Accepted for publication in J. Phys. A: Math. and Gen.; 14 pages. The manuscript has been improved to help readers
arxiv created 2005/11/25 · openalex publication_date 2005/12/21 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
The difficulties arising in the investigation of finite-size scaling in d -dimensional O ( n ) systems with strong anisotropy and/or long-range interaction, decaying with the interparticle distance r as r − d −σ (0 < σ ⩽ 2), 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.