The critical point ratio for some d = 2 classical models

The universal critical point ratio of the square of the second moment of the order parameter to its fourth moment, denoted as Q, is exploited to determine the position of the critical Ising transition lines in the phase diagram of the Ashkin-Teller (AT) model on the square lattice. A leading-order expansion of the Q ratio in the presence of a non-vanishing thermal field is found from finite-size scaling and the corresponding expression is fitted to the accurate perturbative transfer-matrix data for the L x L squaxe clusters with L <= 9. The same method is used to determine the critical Ising transition line on the phase diagram of the Blume-Capel (BC) model (L <= 11). We have also calculated the Q ratio for the q=3 Potts model in the critical point. The previously predicted scaling relation for this universality class is confirmed by our results for L <= 12.status: publishe