  Transfer-matrix scaling methods have been used to study critical properties
of field-induced phase transitions of two distinct two-dimensional
antiferromagnets with discrete-symmetry order parameters: triangular-lattice
Ising systems (TIAF) and the square-lattice three-state Potts model (SPAF-3).
Our main findings are summarised as follows. For TIAF, we have shown that the
critical line leaves the zero-temperature, zero -field fixed point at a finite
angle. Our best estimate of the slope at the origin is $(dT_c/dH)_{T=H=0} =
4.74 \pm 0.15$. For SPAF-3 we provided evidence that the zero-field correlation
length diverges as $\xi(T \to 0, H=0) \simeq \exp (a/T^{x})$, with $x=1.08 \pm
0.13$, through analysis of the critical curve at $H \neq 0$ 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) $H \neq
0: c=1/2, \eta=1/4$.
