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 $R<\mathrm{}0\mathrm{}$ only an antiferromagnetically ordered phase exists. Its transition to the disordered phase is first order for temperatures below the tricritical point ($T_t$,$H_t$). For $R\to 0$ also $T_t\to 0$. For $R=0\mathrm{}$ we find very good agreement with the results of Müller-Hartmann and Zittartz. For $R>\mathrm{}0\mathrm{}$ and $H_1<H<\mathrm{}{H}_2$ 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 $T=0\mathrm{}$, such that for $T>\mathrm{}0\mathrm{}$ 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 $R\to \frac{1}{2}$ and $H<\mathrm{}{H}_1$ the regime of the antiferromagnetic phases goes to zero temperature, while for $R>\mathrm{}\frac{1}{2}$ the superantiferromagnetic phase exists also for $H<\mathrm{}{H}_1$. 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 $T=0\mathrm{}$ is related to known results on hard-core lattice gases. It is shown that it is useful to interpret the transitions at $T=0\mathrm{}$ 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.