Azhari Mouhcine, Yu Unjong
Fakultät für Mathematik und Naturwissenschaften Bergische Universität Wuppertal, 42097 Wuppertal, Germany and Laboratory of High Energy Physics and Condensed Matter, Hassan II University-Casablanca, Faculty of Sciences Aïn-Chock, 5366 Maarif, Casablanca 20100, Morocco.
Department of Physics and Photon Science, Gwangju Institute of Science and Technology, Gwangju 61005, South Korea.
Phys Rev E. 2020 Oct;102(4-1):042113. doi: 10.1103/PhysRevE.102.042113.
We investigate the mixed-spin Blume-Capel model with spin-1/2 and spin-S (S=1, 2, and 3) on the simple cubic and body-centered cubic lattices with single-ion-splitting crystal field (Δ) by using the Metropolis and the Wang-Landau Monte Carlo methods. We show that the two methods are complementary: The Wang-Landau algorithm is efficient to construct phase diagrams and the Metropolis algorithm allows access to large-sized lattices. By numerical simulations, we prove that the tricritical point is independent of S for both lattices. The positions of the tricritical point in the phase diagram are determined as [Δ_{t}/J=2.978(1); k_{B}T_{t}/J=0.439(1)] and [Δ_{t}/J=3.949(1); k_{B}T_{t}/J=0.854(1)] for the simple cubic and the body-centered cubic lattices, respectively. A very strong supercritical slowing down and hysteresis were observed in the Metropolis update close to first-order transitions for Δ>Δ_{t} in the body-centered cubic lattice. In addition, for both lattices we found a line of compensation points, where the two sublattice magnetizations have the same magnitude. We show that the compensation lines are also S independent.
我们使用Metropolis方法和Wang-Landau蒙特卡罗方法，研究了在具有单离子分裂晶体场（Δ）的简单立方晶格和体心立方晶格上，自旋为1/2和自旋为S（S = 1、2和3）的混合自旋Blume-Capel模型。我们表明这两种方法是互补的：Wang-Landau算法在构建相图方面效率很高，而Metropolis算法能够处理大尺寸晶格。通过数值模拟，我们证明了对于这两种晶格，三临界点均与S无关。对于简单立方晶格和体心立方晶格，相图中三临界点的位置分别确定为[Δt/J = 2.978(1); kB Tt/J = 0.439(1)]和[Δt/J = 3.949(1); kB Tt/J = 0.854(1)]。在体心立方晶格中，当Δ>Δt时，在接近一级相变的Metropolis更新中观察到非常强烈的超临界慢化和磁滞现象。此外，对于这两种晶格，我们都发现了一条补偿点线，其中两个亚晶格磁化强度大小相同。我们表明补偿线也与S无关。
