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Finite-size correlation length and violations of finite-size scaling

Author

Listed:
  • S. Caracciolo

    (Scuola Normale Superiore and INFN)

  • A. Gambassi

    (Scuola Normale Superiore and INFN)

  • M. Gubinelli

    (Università degli Studi di Pisa)

  • A. Pelissetto

    (Università degli Studi di Roma “La Sapienza")

Abstract

We address the problem of the definition of the finite-volume correlation length. First, we study the large-N limit of the N-vector model, and we show the existence of several constraints on the definition if regularity of the finite-size scaling functions and correct anomalous behaviour above the upper critical dimension are required. Then, we study in detail a model in which the zero mode is prohibited. Such a model is a generalization of the fixed-magnetization Ising model which is equivalent to the lattice gas. Also in this case, we find that the finite-volume correlation length must satisfy appropriate constraints in order to obtain regular finite-size scaling functions, and, above the upper critical dimension, an anomalous scaling behaviour. The large-N results are confirmed by a one-loop calculation in the lattice φ4 theory.

Suggested Citation

  • S. Caracciolo & A. Gambassi & M. Gubinelli & A. Pelissetto, 2001. "Finite-size correlation length and violations of finite-size scaling," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 20(2), pages 255-265, March.
    • Handle: RePEc:spr:eurphb:v:20:y:2001:i:2:d:10.1007_bf01352587
    DOI: 10.1007/BF01352587
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