论文标题
简单立方晶格上广义二十面体模型的蒙特卡洛研究
Monte Carlo study of a generalized icosahedral model on the simple cubic lattice
论文作者
论文摘要
我们研究了简单的立方晶格上广义二十面体模型的临界行为。二十面体模型的场变量可能采用十二个单位长度的向量之一，这是由Icosahedron的归一化顶点给出的，作为值。与Blume-Capel模型类似，除了iSing模型中，除了$ -1 $和$ 1 $之外，旋转可能会采用$ 0 $的值，我们将其作为允许的值添加为广义模型$（0,0,0）$。有一个参数$ d $可以控制这些空隙的密度。对于一定范围的$ d $，该型号经历了二阶相变。在关键线上，出现$ O（3）$对称。此外，我们证明在此范围内，类似于简单的立方晶格上的Blume-Capel模型，有一个$ D $的值，导致缩放缩放的校正消失。我们通过使用本地大都市和集群更新的混合体，对线性尺寸的晶格进行蒙特卡洛模拟。研究这种特定模型的动机主要是技术性质。与在微观级别上具有$ O（3）$对称性的模型相比，所需的内存时间和CPU时间更少。由于有限大小的缩放分析，我们获得了$ν= 0.71164（10）$，$η= 0.03784（5）$，$ω= 0.759（2）$，用于三维Heisenberg普遍性类别的关键指数。与破坏$ o（3）$对称性相关的无关重新归一化组特征值的估计值为$ y_ {ico} = -2.19（2）$。
We study the critical behavior of a generalized icosahedral model on the simple cubic lattice. The field variable of the icosahedral model might take one of twelve vectors of unit length, which are given by the normalized vertices of the icosahedron, as value. Similar to the Blume-Capel model, where in addition to $-1$ and $1$, as in the Ising model, the spin might take the value $0$, we add in the generalized model $(0,0,0)$ as allowed value. There is a parameter $D$ that controls the density of these voids. For a certain range of $D$, the model undergoes a second-order phase transition. On the critical line, $O(3)$ symmetry emerges. Furthermore, we demonstrate that within this range, similar to the Blume-Capel model on the simple cubic lattice, there is a value of $D$, where leading corrections to scaling vanish. We perform Monte Carlo simulations for lattices of a linear size up to $L=400$ by using a hybrid of local Metropolis and cluster updates. The motivation to study this particular model is mainly of technical nature. Less memory and CPU time are needed than for a model with $O(3)$ symmetry at the microscopic level. As the result of a finite-size scaling analysis we obtain $ν=0.71164(10)$, $η=0.03784(5)$, and $ω=0.759(2)$ for the critical exponents of the three-dimensional Heisenberg universality class. The estimate of the irrelevant renormalization group eigenvalue that is related with the breaking the $O(3)$ symmetry is $y_{ico}=-2.19(2)$.
