论文标题
蒙特卡洛研究对非规范二维和三维晶格的Blume-Capel模型：相图，三临界和关键指数
Monte Carlo studies of the Blume-Capel model on nonregular two- and three-dimensional lattices: Phase diagrams, tricriticality, and critical exponents
论文作者
论文摘要
我们执行蒙特卡洛模拟，结合了Wang-Landau和Metropolis算法，以研究Blume-Capel模型的相图，以不同类型的非量化晶格（Lieb Lattice（LL），装饰的三角形晶格（DTL）和装饰的简单Cubic Cubic Lattice（DSC））。晶格的不规则特征在相图的区域中诱导双重转变（重进入行为），在该区域中，相变的性质从一阶变为二阶变化。提出了这种重新进入的物理机制。大规模的蒙特卡洛模拟是通过有限尺寸的缩放分析进行的，以计算三种各向异性值$Δ/j \ in \ big \ big \ {0，1，1，1，1，1.34 \ textrm {（for ll ll）}，1.51 \ textrm {fextrm {（gim textrm）的关键指数和关键粘合剂累积累积。因此，在两个维度和三个维度上与标准ISING通用类别没有偏差。我们还报告了三项点点的位置至可观的精确度：（$Δ_T/j = 1.3457（1）$; $ k_b t_t/j = 0.309（2）$），（$δ_t/j = 1.5766（1）$; $ k_b t_t t_t/j = 0.481 $; $ k_b t_t/j = 0.569（4）$）分别为LL，DTL和DSC。
We perform Monte Carlo simulations, combining both the Wang-Landau and the Metropolis algorithms, to investigate the phase diagrams of the Blume-Capel model on different types of nonregular lattices (Lieb lattice (LL), decorated triangular lattice (DTL), and decorated simple cubic lattice (DSC)). The nonregular character of the lattices induces a double transition (reentrant behavior) in the region of the phase diagram at which the nature of the phase transition changes from first-order to second-order. A physical mechanism underlying this reentrance is proposed. The large-scale Monte Carlo simulations are performed with the finite-size scaling analysis to compute the critical exponents and the critical Binder cumulant for three different values of the anisotropy $Δ/J \in \big\{ 0, 1, 1.34 \textrm{ (for LL)}, 1.51 \textrm{ (for DTL and DSC)} \big\}$, showing thus no deviation from the standard Ising universality class in two and three dimensions. We report also the location of the tricritical point to considerable precision: ($Δ_t/J=1.3457(1)$; $k_B T_t/J=0.309(2)$), ($Δ_t/J=1.5766(1)$; $k_B T_t/J=0.481(2)$), and ($Δ_t/J=1.5933(1)$; $k_B T_t/J=0.569(4)$) for LL, DTL, and DSC, respectively.
