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Numerical simulations of random spin (and fermionic) models with a wide distribution of energy scales

机译：具有广泛能级分布的随机自旋（和费米离子）模型的数值模拟

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The magnetic behavior of semiconductors doped with randomly distributed magnetic elements (such as iron or manganese) and/or bound carriers (such as phosphorus or boron in silicon) are described by many-body Hamiltonians with a broad distribution of coupling constants and energy scales. These wide distributions (covering several orders of magnitude in some cases) lead to unusual properties, such as strong suppression of magnetic phase transitions due to quantum fluctuations, unusual thermodynamic behavior in the magnetically ordered phase, etc. The wide distributions also pose several challenges to both analytical and computational approaches used to calculate the physical properties of such systems. We describe some of the techniques that have been applied successfully to such systems, including numerical renoramlization group as well as Monte Carlo methods. Examples are drawn from lightly doped conventional semiconductors [Si, Ge] as well as diluted magnetic semiconductors [such as (Cd, Mn)Te and (Ga,Mn)As]. Extension of these methods to diluted magnetic semiconductors in the metallic regime with itinerant carriers (fermionic degrees of freedom) is also discussed.
机译：多体哈密顿量描述了掺杂有随机分布的磁性元素（例如铁或锰）和/或键合载流子（例如硅中的磷或硼）的半导体的磁行为，这些耦合常数和能级分布范围很广。这些宽分布（在某些情况下覆盖几个数量级）会导致异常的特性，例如由于量子涨落而对磁相变的强烈抑制，在磁有序相中的异常热力学行为等。用于计算此类系统物理特性的分析和计算方法。我们描述了一些已成功应用于此类系统的技术，包括数值重新定级化组以及蒙特卡洛方法。例子从轻掺杂的常规半导体[Si，Ge]以及稀释的磁性半导体[例如（Cd，Mn）Te和（Ga，Mn）As]中得出。还讨论了将这些方法扩展到具有流动性载流子（铁离子自由度）的金属状态下的稀磁半导体。

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