Field-induced ordering in critical antiferromagnets

Transfer-matrix scaling methods have been used to study critical properties of field-induced phase transitions of two distinct two-dimensional antifer romagnets with discrete-symmetry order parameters: triangular-lattice Ising systems (TIAF) and the square-lattice three-state Potts model (SPAF-3). Ou r main findings are summarized as follows. For TIAF, we have shown that the critical line leaves the zero-temperature, zero-field fixed point at a fin ite angle. Our best estimate of the slope at the origin is (dT(c)/dH)(T=H=0 )=4.74+/-0.15. For SPAF-3 we provided evidence that the zero-field correlat ion length diverges as xi(T --> 0, H = 0) similar or equal to exp(a/T-x), w ith x = 1.08 +/- 0.13, through analysis of the critical curve at H not equa l 0 plus crossover arguments. For SPAF-3 we have also ascertained that the conformal anomaly and decay-of-correlations exponent behave as (a) H = 0:c = 1, eta = 1/3. (b) H not equal 0:c = 1/2, eta = 1/4. [S1063-651X(99)11403- X].