Scaling behavior of a square-lattice Ising model with competing interactions in a uniform field

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 exponents. 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 $\eta=1/4$, $\gamma/\nu=7/4$, $\beta/\nu=1/8$ are found. For higher fields, on the line separating row-shifted $(2 \times 2)$ and disordered phases, we find values of the exponent $\eta$ very close to zero.