论文标题
偶极玻璃和休闲铁电行为的模型
Model for Dipolar Glass and Relaxor Ferroelectric Behavior
论文作者
论文摘要
热浴蒙特卡洛模拟已用于研究具有随机场类型的12态的Heisenberg模型，用于几个随机性耦合参数$ H_R $的值。 12个状态对应于立方体的[110]方向。使用周期性边界条件的简单尺寸$ 128 \ times 128 $的简单立方晶格，并研究了32个样品的每个值$ h_r $。该模型具有带有耦合能量$ j $的标准非随机两旋式交换术语，并且一个字段为12个旋转状态中的两个添加了能量$ h_r $，在每个站点中随机和独立地选择。我们为$ H_R / J = $ -2.5，-2.0，-1.5、3.0和4.0提供结果。对于所有这些情况，除$ h_r / j = $ -2.5以外，我们看到在温度$ t_c $的情况下，特定的热量和纵向敏感性在温度下明显清晰。在$ t_c $，结构因子中的峰值行为，$ s（{\ bf k}）$，小$ | {\ bf k} | $是日志图图上的一条直线。但是，对于$ h_r / j = $ -1.5和3.0，此行的斜率值不同于$ h_r / j = $ -2.0和4.0。我们认为，前两种情况正在显示弱随机场中立方固定点的行为，第二个情况的行为显示了当Imry-MA长度小于样本量时，各向同性固定点的行为。这些$ L = 128 $的样品低于$ t_c $，显示了铁电顺序，随着$ t $的减少，该订单迅速沿八个[111]方向之一定向。排序方向的旋转是由立方各向异性引起的。对于$ h_r / j = $ -2.5，我们看不到单个定义明确的$ t_c $的明确证据。
Heat bath Monte Carlo simulations have been used to study a 12-state discretized Heisenberg model with a type of random field, for several values of the randomness coupling parameter $h_R$. The 12 states correspond to the [110] directions of a cube. Simple cubic lattices of size $128 \times 128 \times 128$ with periodic boundary conditions were used, and 32 samples were studied for each value of $h_R$. The model has the standard nonrandom two-spin exchange term with coupling energy $J$ and a field which adds an energy $h_R$ to two of the 12 spin states, chosen randomly and independently at each site. We provide results for the cases $h_R / J =$ -2.5, -2.0, -1.5, 3.0 and 4.0. For all these cases except $h_R / J =$ -2.5, we see an apparently sharp phase transition at a temperature $T_c$ where the specific heat and the longitudinal susceptibility are peaked. At $T_c$, the behavior of the peak in the structure factor, $S ({\bf k} )$, at small $|{\bf k}|$ is a straight line on a log-log plot. However, the value of the slope of this line is different for $h_R /J =$ -1.5 and 3.0 than it is for $h_R / J =$ -2.0 and 4.0. We believe that the first two cases are showing the behavior of a cubic fixed point in a weak random field, and the behavior of the second two cases are showing the behavior of an isotropic fixed point when the Imry-Ma length is smaller than the sample size. Below $T_c$, these $L = 128$ samples show ferroelectric order, and this order rapidly becomes oriented along one of the eight [111] directions as $T$ is reduced. This rotation of the ordering direction is caused by the cubic anisotropy. For $h_R / J =$ -2.5, we do not see clear evidence of a single well-defined $T_c$.
