NONUNIVERSAL CRITICAL-BEHAVIOR OF THE 2-DIMENSIONAL ISING-MODEL WITH CROSSING BONDS

The two-dimensional square lattice Ising model with the nearest-neighbour ferromagnetic interaction J and the next-nearest-neighbour antiferromagnetic interaction J' is investigated in the interaction range \J/J'\ less-than-or-equal-to 0.8. This model is shown to violate the ordinary universality hypothesis. Estimations of critical temperature as a function of J/J' by means of an extrapolation method results in the exact critical temperature T(c)* when \J/J'\ = 0 and in an approximate T(c) accurate up to the fourth digit when \J/J'\ is small. The critical exponent gamma is estimated as a function of \J/J'\ with the use of the multi-effective-field theory and the coherent-anomaly method. It is shown, consequently, that gamma varies continuously as \J/J'\ increases.