CROSS-OVER AND EFFECTIVE SCALING DIMENSIONS

M. A. Novotny
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M. A. Novotny: Supercomputer Computations Research Institute, Florida State University, Tallahassee, Florida 32306-4052, USA;

International Journal of Modern Physics C (IJMPC), 1996, vol. 07, issue 03, 361-370

Abstract: Although cross over between fixed points associated with different universality classes is a ubiquitious phenomena, there is little theoretical insight and less numerical evidence about exactly how cross-over phenomena occur. Here numerical evidence for the picture that cross-over phenomena are governed by the underlying structure of the associated renormalization group is given. In particular, it is shown how the cross-over is related to the effective dimension from scaling of the system. For the ferromagnetic Ising model in two and three dimensions numerical evidence will be presented that the cross-over is governed by the line of fixed points in non-integer dimensions. This allows for successful comparisons between the effective dimension from scaling for finite systems and expansions in dimension of universal quantities such as critical exponents.

Date: 1996
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DOI: 10.1142/S0129183196000302

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