Hintermann-Merlini模型的临界性质
Critical properties of the Hintermann-Merlini model
摘要：
Hintermann-Merlini模型的许多重要性质都是通过映射到八顶点模型得到的。Wu [J. Phys. C { \bf 8}，2262（1975）]通过将模型的自发磁化强度分别与八顶点模型的非对称自发磁化强度和极化强度联系起来，计算了两个亚晶格上模型的自发磁化强度。后一个猜想仍然没有得到证实。在本文中，我们数值研究的临界特性的模型通过一个有限尺寸标度分析的基础上的传输矩阵计算和蒙特卡罗模拟。模型的所有解析预测都被我们的数值结果所证实。中心荷$c=1$被发现的临界流形调查。此外，还研究了该模型的一些不可预测的几何性质。确定了两个子晶格上最大伊辛团簇的分形维数。子格点A上最大伊辛团簇的分形维数取固定值$D_{\rm a}=1.888(2)$，而子格点B上最大伊辛团簇的分形维数随模型参数连续变化。
英文摘要：
Many critical properties of the Hintermann-Merlini model are known exactly through the mapping to the eight-vertex model. Wu [J. Phys. C {\bf 8}, 2262 (1975)] calculated the spontaneous magnetizations of the model on two sublattices by relating them to the conjectured spontaneous magnetization and polarization of the eight-vertex model, respectively. The latter conjecture remains unproved. In this paper, we numerically study the critical properties of the model by means of a finite-size scaling analysis based on transfer matrix calculations and Monte Carlo simulations. All analytic predictions for the model are confirmed by our numerical results. The central charge $c=1$ is found for the critical manifold investigated. In addition, some unpredicted geometry properties of the model are studied. Fractal dimensions of the largest Ising clusters on two sublattices are determined. The fractal dimension of the largest Ising cluster on the sublattice A takes fixed value $D_{\rm a}=1.888(2)$, while that for sublattice B varies continuously with the parameters of the model.
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