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Failure of universal finite-size scaling above the upper critical dimension

Author

Listed:
  • Chen, X.S.
  • Dohm, V.

Abstract

Previous theories have predicted that O(n) symmetric systems in a finite cubic geometry with periodic boundary conditions have universal finite-size scaling functions near criticality in d>4 dimensions. On the basis of exact results for the O(n) symmetric ϕ4 model in the large n limit we show that universal finite-size scaling does not hold in the predicted form because of significant cut-off and lattice effects for d>4. It is shown that finite-size scaling is valid with two reference lengths which turn out to be identical with the amplitudes of the bulk correlation length. For the ϕ4 field theory the finite-size scaling functions are shown to be non-universal, i.e., to depend explicitly on the cut-off and on the bare four-point coupling constant, whereas for a ϕ4 lattice model the finite-size scaling functions have a different form that is independent of the lattice spacing and the four-point coupling constant.

Suggested Citation

  • Chen, X.S. & Dohm, V., 1998. "Failure of universal finite-size scaling above the upper critical dimension," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 251(3), pages 439-451.
    • Handle: RePEc:eee:phsmap:v:251:y:1998:i:3:p:439-451
    DOI: 10.1016/S0378-4371(97)00688-2
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