Krcmar R, Iharagi T, Gendiar A, Nishino T
Institute of Electrical Engineering, Centre of Excellence CENG, Slovak Academy of Sciences, Dúbravská cesta 9, SK-841 04, Bratislava, Slovakia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Dec;78(6 Pt 1):061119. doi: 10.1103/PhysRevE.78.061119. Epub 2008 Dec 17.
The ferromagnetic-paramagnetic phase transition of the two-dimensional frustrated Ising model on a hyperbolic lattice is investigated by use of the corner transfer matrix renormalization group method. The model contains a ferromagnetic nearest-neighbor interaction J1 and a competing antiferromagnetic interaction J2 . A mean-field-like second-order phase transition is observed when the ratio kappa=J_{2}J_{1} is less than 0.203. In the region 0.203<kappa<14 , the spontaneous magnetization is discontinuous at the transition temperature. Such tricritical behavior suggests that the phase transitions on hyperbolic lattices need not always be mean-field-like.
利用角转移矩阵重整化群方法研究了双曲晶格上二维受挫伊辛模型的铁磁 - 顺磁相变。该模型包含铁磁最近邻相互作用(J1)和竞争反铁磁相互作用(J2)。当比率(\kappa = J_{2} / J_{1})小于(0.203)时，观察到类似平均场的二阶相变。在(0.203 < \kappa < 14)的区域中，自发磁化强度在转变温度处是不连续的。这种三临界点行为表明双曲晶格上的相变不一定总是类似平均场的。
