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.
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Received 26 January 1999 and Received in final form 25 October 1999
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Dubrulle, B. Finite size scale invariance. Eur. Phys. J. B 14, 757–771 (2000). https://doi.org/10.1007/s100510051087
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DOI: https://doi.org/10.1007/s100510051087