Field-driven transition in an Ising magnet with mixed interactions

Transfer-matrix methods are used, in conjunction with finite-size scaling and conformal invariance concepts, to generate an accurate phase diagram for a two-dimensional square-lattice Ising spin-1/2 magnet, with couplings which are positive along one coordinate axis, and negative along the other, in a uniform external field. Our results indicate that the critical line starts horizontally at the zero-temperature end of the phase boundary, at variance with the reentrant behavior predicted in some earlier studies. Estimates of the thermal scaling exponent are very close to the Ising value $y_T=1$ along the critical line, except near T=0 where strong crossover effects prevent a reliable analysis.