Ashkin-Teller and Gross-Neveu models: New relations and results

Abstract

It is shown that (i) the N-component Ashkin-Teller model in d=2 has continuous O(N) symmetry, (ii) its critical properties near the decoupled Ising transition are determined by the massive Gross-Neveu [(ψ¯ψ${)}^2$] model in general and the (integrable) massless version along a line, (iii) the known results for the massless Gross-Neveu model imply that the first-order transition found as N→∞ persists down to N=3 along this line, (iv) the supersymmetry of the N=3 model implies that the leading singularity of the free energy is zero along the first-order line, and (v) the N=4 model along this line decouples into two identical N=2 models up to subleading corrections.