Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, 1 Svientsitskii Street, 79011 Lviv, Ukraine.
J Phys Condens Matter. 2013 Oct 9;25(40):406003. doi: 10.1088/0953-8984/25/40/406003. Epub 2013 Sep 11.
A complete solution of the ground-state problem for the Ising model on an anisotropic triangular lattice with the nearest-neighbor interactions in a magnetic field is presented. It is shown that this problem can be reduced to the ground-state problem for an infinite chain with the interactions up to the second neighbors. In addition to the known ground-state structures (which correspond to full-dimensional regions in the parameter space of the model), new structures are found (at the boundaries of these regions), in particular, zigzagging stripes similar to those observed experimentally in colloidal monolayers. Though the number of parameters is relatively large (four), all the ground-state structures of the model are constructed and analyzed and therefore the paper can be considered as an example of a complete solution of a ground-state problem for classical spin or lattice-gas models. The paper can also help to verify the correctness of some results obtained previously by other authors and concerning the ground states of the model under consideration.
给出了各向异性三角格子上最近邻相互作用的磁场中伊辛模型基态问题的完全解。结果表明，该问题可以简化为具有次近邻相互作用的无限链的基态问题。除了已知的基态结构（对应于模型参数空间的全维区域）外，还发现了新的结构（在这些区域的边界处），特别是类似于胶体单层中实验观察到的锯齿条纹。尽管参数数量相对较多（四个），但模型的所有基态结构都已构建和分析，因此本文可以被视为经典自旋或格气模型基态问题完全解的一个范例。本文还可以帮助验证其他作者之前获得的一些关于所考虑模型基态的结果的正确性。
