Eur. Phys. J. B 20, 255-265 (2001)
https://doi.org/10.1007/BF01352587

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

¹ Scuola Normale Superiore and INFN -Sezione di Pisa, 56100 Pisa, Italia
² Dipartimento di Fisica and INFN -Sezione di Pisa, Università degli Studi di Pisa, 56100 Pisa, Italia
³ Dipartimento di Fisica and INFN -Sezione di Roma I, Università degli Studi di Roma "La Sapienza", 00185 Roma, Italia

Corresponding authors: ^a sergio.caracciolo@sns.it - ^b andrea.gambassi@sns.it - ^c mgubi@cibs.sns.it - ^d andrea.pelissetto@roma1.infn.it

Received: 31 October 2000
Revised: 21 December 2000
Published online: 15 March 2001

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 theory.