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

We address the problem of the definition of the finite-volume correlation l ength. 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 th e finite-size scaling functions and correct anomalous behaviour above tile upper critical dimension are required. Then, we study in detail a model in which tile zero mode is prohibited. Such. a model is a generalization of th e fixed-magnetization Ising model which is equivalent to the lattice gas. A lso in this case, we find that tile finite-volume correlation length must s atisfy appropriate constraints in order to obtain regular finite-size scali ng functions, and, above the upper critical dimension, an anomalous scaling behaviour. The large-N results are confirmed by a one-loop calculation in tile lattice phi (4) theory.