N-color Ashkin-Teller model

Abstract

We study a model Hamiltonian consisting of $N$ Ising models coupled pairwise through a four-spin interaction $K_4$. When $N=2\mathrm{}$ this model is the well-known Ashkin-Teller model which shows nonuniversal critical behavior in two dimensions in the neighborhood of $K_4=0\mathrm{}$. To see if this behavior persists for $N\ne 2$ we perform a first-order-perturbation expansion around the decoupling point in two dimensions. As an aid in interpreting the results of this perturbation expansion we have determined the phase diagram of the system through mean-field theory and Monte Carlo studies in both two and three dimensions for $N=3\mathrm{}$. The results show that $N=2\mathrm{}$ is special because the coupling between Ising models is marginal over a range of values of $K_4$. We discuss the effect of the coupling $K_4$ for $N\ne 2$.