Eur. Phys. J. B 14, 757-771 (2000)
https://doi.org/10.1007/s100510051087

Finite size scale invariance

NCAR, P.O. Box 3000, Boulder, CO 80307-3000, USA and Observatoire Midi-Pyrénées, 14 avenue Belin, 31400 Toulouse, France

Received: 26 January 1999
Revised: 25 October 1999
Published online: 15 April 2000

Abstract

We develop a new approach to scale symmetry, which takes into account the possible finite cut-offs of the fields or the parameters. This new symmetry, called finite size scale symmetry: i) includes the traditional self-similarity as a limiting case, when the cut-offs are set to infinity (infinite size-system); ii) is consistent with the traditional finite size scaling approach already used in critical phenomena; iii) enables the computation of some of the universal functions appearing in the finite size scaling formulation; iv) allows scale transformations leaving the cut-offs invariant, like in the traditional renormalization approach; v) can be formulated to allow for positive or negative fields and parameters; vi) leads to new predictions about the shape of some distributions in critical phenomena or turbulence which are in very good agreement with the experimental or numerical findings.