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 x 2) and disordered phases, we find values of the exponent eta very close to zero.