Finite-Size Correlation Length and Violations of Finite-Size Scaling

Sergio Caracciolo, Andrea Gambassi, Massimiliano Gubinelli and Andrea Pelissetto

First issued 30 October 2000 · PDF

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 in 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 $\phi^4$ theory.

Versions

1. Version 1 (arXiv v1) current
   30 October 2000
   arXiv comments: 19 pages, Latex2e
   PDF · LaTeX source · files and digests · arXiv:cond-mat/0010479

Cite

Sergio Caracciolo, Andrea Gambassi, Massimiliano Gubinelli and Andrea Pelissetto. Finite-Size Correlation Length and Violations of Finite-Size Scaling. Papers of Massimiliano Gubinelli, 2000, version 1. https://mgubi.org/papers/paper/finite-size-scaling-violations/

Licence: arXiv.org non-exclusive license to distribute, assumed for submissions of 1991-2003; all other rights reserved to the authors

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