Fu Zhe, Guo Wenan, Blöte Henk W J
College of Physics and Electronic Engineering, Xinxiang University, Xinxiang 453003, China.
Physics Department, Beijing Normal University, Beijing 100875, China and Beijing Computational Science Research Center, Beijing 100193, China.
Phys Rev E. 2020 Jan;101(1-1):012118. doi: 10.1103/PhysRevE.101.012118.
We study phase transitions of the Potts model on the centered-triangular lattice with two types of couplings, namely, K between neighboring triangular sites, and J between the centered and the triangular sites. Results are obtained by means of a finite-size analysis based on numerical transfer-matrix calculations and Monte Carlo simulations. Our investigation covers the whole (K,J) phase diagram, but we find that most of the interesting physics applies to the antiferromagnetic case K<0, where the model is geometrically frustrated. In particular, we find that there are, for all finite J, two transitions when K is varied. Their critical properties are explored. In the limits J→±∞ we find algebraic phases with infinite-order transitions to the ferromagnetic phase.
我们研究了具有两种耦合的中心三角晶格上的Potts模型的相变，即相邻三角格点之间的K耦合，以及中心格点与三角格点之间的J耦合。通过基于数值转移矩阵计算和蒙特卡罗模拟的有限尺寸分析得到了结果。我们的研究涵盖了整个（K，J）相图，但我们发现大多数有趣的物理现象适用于反铁磁情况K<0，此时模型存在几何阻挫。特别地，我们发现，对于所有有限的J，当K变化时会有两个转变。我们探索了它们的临界性质。在J→±∞的极限情况下，我们发现了向铁磁相转变的具有无穷阶转变的代数相。
