Monte Carlo calculation of order on the triangular Ising lattice with next-nearest-neighbor interactions

Abstract

This paper presents a comparison of Monte Carlo calculations with the corresponding Bethe-Peierls solution of Campbell and Schick for an Ising-spin system on a triangular lattice with antiferromagnetic nearest-neighbor and ferromagnetic next-nearest-neighbor interactions. The results agree for nonzero external field at a density of one-third. But for zero external field at temperatures below $\frac{\mathrm{kT}}{2J}=0.5$ with densities between one-third and two-thirds, the Monte Carlo calculations differ from the Bethe-Peierls solution. This is probably due to the absence of pair-pair correlations in the latter.