论文标题
经典旋转1 ising模型的批判行为：组合的低温序列扩展和大都市蒙特卡洛分析
Critical behavior of the classical spin-1 Ising model: a combined low-temperature series expansion and Metropolis Monte Carlo analysis
论文作者
论文摘要
在本文中，我们从理论上使用两种方法从理论上研究了经典的自旋-1 ising模型的临界特性：1）分析性低温序列膨胀和2）数值大都会蒙特卡洛技术。在此分析中，我们讨论了由第一邻居Spin-1 Ising模型建模的一，二维和三维系统的临界行为，用于不同类型的交换相互作用。根据Metropolis Monte Carlo模拟获得的结果的比较使我们能够突出广泛使用的均值场理论方法的限制。我们还通过一个简单的转换表明，对于特殊情况，双线性和双音节项在哈密顿量中设置了等于零，可以将Spin-1 Ising模型的分配函数降低到Spin-1/2 Ising模型的分配函数，该模型具有与温度相关的外部场和温度独立的交换时间，该互动是根据该测量的其他指数，并根据该元素进行了数字，并使用hamilton norser进行了验证。最后，我们研究了临界温度对Ising Hamiltonian中远程相互作用强度的依赖性，将其与第一邻居Spin-1/2 ISING模型进行了比较。
In this paper, we theoretically study the critical properties of the classical spin-1 Ising model using two approaches: 1) the analytical low-temperature series expansion and 2) the numerical Metropolis Monte Carlo technique. Within this analysis, we discuss the critical behavior of one-, two- and three-dimensional systems modeled by the first-neighbor spin-1 Ising model for different types of exchange interactions. The comparison of the results obtained according the Metropolis Monte Carlo simulations allows us to highlight the limits of the widely used mean-field theory approach. We also show, via a simple transformation, that for the special case where the bilinear and bicubic terms are set equal to zero in the Hamiltonian the partition function of the spin-1 Ising model can be reduced to that of the spin-1/2 Ising model with temperature dependent external field and temperature independent exchange interaction times an exponential factor depending on the other terms of the Hamiltonian and confirm this result numerically by using the Metropolis Monte Carlo simulation. Finally, we investigate the dependence of the critical temperature on the strength of long-range interactions included in the Ising Hamiltonian comparing it with that of the first-neighbor spin-1/2 Ising model.
