  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.
