Monte Carlo data for a simple cubic Ising antiferromagnet with nearest- and next-nearest-neighbor interactions reveal asymptotic tricritical behavior of the order parameter which is mean-field-like modified by logarithmic corrections and high-temperature susceptibilities which are mean-field-like without corrections, in agreement with renormalization-group calculations. Crossover between tricritical and critical behavior is observed in the temperature variation of the order parameter and high-temperature susceptibility.
The Ising square lattice model with nearest-neighbor (nn) interactions (
J1) is one of the few exactly solvable models [1]. Adding next-neareast- neighbor (nnn) interactions (
J2) or a magnetic field (or both) leads to the non solvability of the model and only some approximate solutions are possible. In this brief report we will review some results obtained within effective field theory. We will show that besides second-order transitions there are also lines of first-order transitions and the coordinates of tricritical points are calculated.
We employ the Monte Carlo method to provide a computer description of the thermodynamic properties of the disordered antiferromagnetic Ising model for a simple cubic lattice with allowance for the nearest neighbors interaction and the next-nearest neighbors interaction. We construct the phase diagram for the model in an external magnetic field for systems with spin concentrations p =1.0, 0.95, and 0.8. We also establish the tricritical behavior of the model. Finally, we study the critical behavior of the model in weak fields.
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 $R\ensuremath{\rightarrow}0$ also ${T}_{t}\ensuremath{\rightarrow}0$. 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 \ifmmode\times\else\texttimes\fi{} 2) superstructure but with many antiphase domain boundaries. For $R\ensuremath{\rightarrow}\frac{1}{2}$ and
H<H1 the regime of the antiferromagnetic phases goes to zero temperature, while for
R>21 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.