Critical properties of the Hintermann-Merlini model.
Many critical properties of the Hintermann-Merlini model are known exactly through the mapping to the eight-vertex model. Wu [J. Phys. C 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 geometric 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 a fixed value D(a)=1.888(2), while that for sublattice B varies continuously with the parameters of the model.
Department of Applied Physics, Anhui University of Technology, Maanshan 243002, China.
Chengxiang
C
Ding
Yancheng
Y
Wang
Wanzhou
W
Zhang
Wenan
W
Guo