Critical line of an n-component cubic model

Abstract

We consider a special case of the n-component cubic model on the square lattice, for which an expansion exists in Ising-like graphs. We construct a transfer matrix and perform a finite-size-scaling analysis to determine the critical points for several values of n. Furthermore we determine several universal quantities, including three critical exponents. For n<2, these results agree well with the theoretical predictions for the critical O(n) branch. This model is also a special case of the ($N_{\alpha },N_{\beta }$) model of Domany and Riedel. It appears that the self-dual plane of the latter model contains the exactly known critical points of the n=1 and 2 cubic models. For this reason we have checked whether this is also the case for 1<n<2. However, this possibility is excluded by our numerical results.

References in corpus (1)

• Surface and bulk transitions in three-dimensional O(n) models

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