Žukovič Milan, Tomita Yusuke, Kamiya Y
Institute of Physics, Faculty of Science, P. J. Šafárik University, Park Angelinum 9, 040 01 Košice, Slovakia.
College of Engineering, Shibaura Institute of Technology, Saitama 337-8570, Japan.
Phys Rev E. 2017 Jul;96(1-1):012145. doi: 10.1103/PhysRevE.96.012145. Epub 2017 Jul 24.
We study critical and magnetic properties of a bilayer Ising system consisting of two triangular planes A and B, with the antiferromagnetic (AF) coupling J_{A} and the ferromagnetic (FM) one J_{B} for the respective layers, which are coupled by the interlayer interaction J_{AB} by using Monte Carlo simulations. When J_{A} and J_{B} are of the same order, the unfrustrated FM plane orders first at a high temperature T_{c1}∼J_{B}. The spontaneous FM order then exerts influence on the other frustrated AF plane as an effective magnetic field, which subsequently induces a ferrimagnetic order in this plane at low temperatures below T_{c2}. When short-range order is developed in the AF plane while the influence of the FM plane is still small, there appears a preemptive Berezinskii-Kosterlitz-Thouless-type pseudocritical crossover regime just above the ferrimagnetic phase transition point, where the short-distance behavior up to a rather large length scale exponentially diverging in ∝J_{A}/T is controlled by a line of Gaussian fixed points at T=0. In the crossover region, a continuous variation in the effective critical exponent 4/9≲η^{eff}≲1/2 is observed. The phase diagram by changing the ratio J_{A}/J_{B} is also investigated.
我们通过蒙特卡罗模拟研究了一个双层伊辛系统的临界和磁性性质，该系统由两个三角形平面A和B组成，各层分别具有反铁磁（AF）耦合(J_{A})和铁磁（FM）耦合(J_{B})，两层通过层间相互作用(J_{AB})耦合。当(J_{A})和(J_{B})处于同一量级时，未受挫的FM平面在高温(T_{c1}\sim J_{B})时首先有序化。然后自发的FM序作为一个有效磁场对另一个受挫的AF平面产生影响，这随后在低于(T_{c2})的低温下在该平面诱导出亚铁磁序。当在AF平面中发展出短程序而FM平面的影响仍然较小时，在亚铁磁相变点上方会出现一个抢先的贝雷津斯基 - 科斯特利茨 - Thouless型伪临界交叉区域，其中在高达相当大的长度尺度上的短距离行为按(\propto J_{A}/T)指数发散，由(T = 0)时的高斯不动点线控制。在交叉区域中，观察到有效临界指数在(4/9\lesssim\eta^{eff}\lesssim1/2)范围内连续变化。还研究了通过改变(J_{A}/J_{B})比值得到的相图。
