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

S. Caracciolo, A. Gambassi, M. Gubinelli and A. Pelissetto
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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"

The European Physical Journal B: Condensed Matter and Complex Systems, 2001, vol. 20, issue 2, 255-265

Abstract: 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.

Keywords: PACS.; 05.70.Jk; Critical; point; phenomena; –; 11.10.Kk; Field; theories; in; dimensions; other; than; four; –; 64.60.-i; General; studies; of; phase; transitions (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1007/BF01352587

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