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We use Monte Carlo and Transfer Matrix methods in combination withextrapolation schemes to determine the phase diagram of the 2Dsuper-antiferromagnetic (SAF) Ising model with next-nearest-neighbor (nnn)interactions in a magnetic field. The interactions between nearest-neighbor(nn) spins are ferromagnetic along x, and antiferromagnetic along y. We findthat for sufficiently low temperatures and fields, there exists a regionlimited by a critical line of 2nd-order transitions separating a SAF phase froma magnetically induced paramagnetic phase. We did not find any region witheither first-order transition or with re-entrant behavior. The nnn couplingsproduce either an expansion or a contraction of the SAF phase. Expansion occurswhen the interactions are antiferromagnetic, and contraction when they areferromagnetic. There is a critical ratio R_c = 1/2 between nnn- andnn-couplings, beyond which the SAF phase no longer exists.

Phase transitions in the two-dimensional super-antiferromagnetic Ising model with next-nearest-neighbor interactions