Transfer-matrix methods, with the help of finite-size scaling and conformal invariance concepts, are used to investigate the critical behavior of two-dimensional square-lattice Ising spin-1/2 systems with first- and second-neighbor interactions, both antiferromagnetic, in a uniform external field. On the critical curve separating collinearly-ordered and paramagnetic phases, our estimates of the conformal anomaly c are very close to unity, indicating the presence of continuously-varying

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... . This is confirmed by direct calculations, which also lend support to a weak-universality picture; however, small but consistent deviations from the Ising-like values η=1/4, γ/ν=7/4, β/ν=1/8 are found. For higher fields, on the line separating row-shifted (2 × 2) and disordered phases, we find values of the exponent η very close to zero.