Evaluation of the correlation length critical exponent of the <i>N</i>‐vector model

Abstract

Abstract An extension of a heuristic treatment of the critical behavior of the Ising model ( N = 1) developed by Thompson, to the general N ‐vector model is made. Two approximations for the correlation length critical exponent v as a function of the lattice spatial dimension d and of the number of components of the order parameter N are obtained. Using the hyperscaling relation, the specific heat critical exponent α is also evaluated. Finally, diagrams are constructed displaying in the plane ( d, N ) various regions, namely: classical critical indexes, non‐classical critical indexes, and no‐phase transition regions or regions where the critical temperature goes to zero. These diagrams are also used to separate regions with divergent specific heat (α &gt; 0) from the ones where it has a cusp‐like behavior (α &lt; 0).