Phase diagrams and critical behavior in Ising square lattices with nearest- and next-nearest-neighbor interactions

The phase diagrams of Ising antiferromagnets in a magnetic field H are investigated for various values of the ratio R between nearest- and next-nearest-neighbor interaction. While meanfield approximations and the existing real-space renormalization-group treatments yield phase diagrams which are sometimes even qualitatively incorrect, accurate results are obtained from Monte Carlo calculations. For $R<0$ only an antiferromagnetically ordered phase exists. Its transition to the disordered phase is first order for temperatures below the tricritical point (Tₜ,Hₜ). For R→0 also Tₜ→0. For $R=0$ we find very good agreement with the results of M\"uller-Hartmann and Zittartz. For $R>0$ and H₁<H<H₂ a new phase with anomalous high ground-state degeneracy is found (two sublattices have only one-dimensional order). These sublattices undergo order-disorder transitions at $T=0$, such that for $T>0$ one is left with a "superantiferromagnetic" phase. At low temperatures in this phase a pronounced tendency is observed to form a simpler (2 ×{} 2) superstructure but with many antiphase domain boundaries. For R→1/2 and H<H₁ the regime of the antiferromagnetic phases goes to zero temperature, while for R>1/2 the superantiferromagnetic phase exists also for H<H₁. The order-disorder transition associated with this phase seems to have non-Ising critical exponents which vary as a function of R and H. Estimates for the exponents lead us to suggest that Suzuki's "weak universality" is valid. The behavior of the model at $T=0$ is related to known results on hard-core lattice gases. It is shown that it is useful to interpret the transitions at $T=0$ as generalized percolation transitions. Since the model may have applications to adsorbate phases in registered structures at (100) surfaces of cubic crystals, the transcription of our results to temperature-coverage phase diagrams and adsorption isotherms is discussed in detail, and possible experimental applications are mentioned.