Singularities near the bifurcation point of the Ashkin-Teller model

Singularities in the $d=2$ Ashkin-Teller model are analyzed by writing down flow equations based upon the Gaussian model in the presence of suitable fields. A scaling function for the coherence length, ξ, is set up in terms of coordinates δ and t which describe deviations from the four-state Potts point. At that point, ξ depends on the reduced temperature as ξ^-1~|t|2/3×|lnt|^-1/2.