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Cross-Over And Effective Scaling Dimensions

Author

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  • M. A. Novotny

    (Supercomputer Computations Research Institute, Florida State University, Tallahassee, Florida 32306-4052, USA;
    Department of Electrical Engineering, 2525 Pottsdamer Street, Florida A&M University–Florida State University, Tallahassee, Florida 32310-6046, USA)

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.

Suggested Citation

  • M. A. Novotny, 1996. "Cross-Over And Effective Scaling Dimensions," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 7(03), pages 361-370.
    • Handle: RePEc:wsi:ijmpcx:v:07:y:1996:i:03:n:s0129183196000302
    DOI: 10.1142/S0129183196000302
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