N-color Ashkin-Teller Model in two dimensions: Solution in the large-N limit

The N-color Ashkin-Teller model is solved exactly in the large-N limit in two dimensions. The phase diagram is found. It is shown that for positive four-spin coupling the transition is first order while for negative four-spin coupling the transition is continuous and Ising type. The specific heat near the second-order transition is calculated and it is found to be finite at the transition because of large corrections to scaling. The latent heat and correlation length at the first-order transition are also calculated.