A Monte Carlo study of the anisotropic N=3 Ashkin–Teller model

The phase diagram of an asymmetric N=3 Ashkin–Teller model is obtained by a numerical analysis which combines Monte Carlo renormalization group and reweighting techniques. Present results reveal several differences with those obtained by mean-field calculations and a Hamiltonian approach. In particular, we found Ising critical exponents along a line where Goldschmidt has located the Kosterlitz–Thouless multicritical point. On the other hand, we did find nonuniversal exponents along another transition line. Symmetry breaking in this case is very similar to the N=2 case, since the symmetries associated to only two of the Ising variables are broken. However, for large values of the coupling constant ratio XW=W/K, when the only broken symmetry is of a hidden variable, we detected first-order phase transitions giving evidence supporting the existence of a multicritical point, as suggested by Goldschmidt, but in a different region of the phase diagram.