FCC和BCC晶格中无序诱导金属-绝缘体相变的临界参数
Critical parameters for the disorder-induced metal-insulator transition in FCC and BCC lattices
摘要：
我们用转移矩阵方法研究了无序诱导的金属-绝缘体相变。我们采用各向同性的最近邻跳跃和均匀分布的无序势.在简单立方晶格的基础上，我们对自然界中常见的体心立方和面心立方晶格进行了数值计算。我们得到的本地化长度从计算的李雅普诺夫指数为不同的系统尺寸。使用有限尺寸标度分析该数据以找到关键参数。我们创建了一个能量无序的两种晶格类型的相图，注意到它是对称的带中心的体心立方晶格，但不为面心立方晶格。我们发现一个临界指数约为1.5-1.6的两种晶格类型的过渡发生在固定的能量或固定的无序，同意先前获得的结果属于相同的正交普适性类的其他系统。我们注意到临界无序度随着最近邻的数量而增加，这与直觉一致。
英文摘要：
We use a transfer-matrix method to study the disorder-induced metal-insulator transition. We take isotropic nearest- neighbor hopping and an onsite potential with uniformly distributed disorder. Following previous work done on the simple cubic lattice, we perform numerical calculations for the body centered cubic and face centered cubic lattices, which are more common in nature. We obtain the localization length from calculated Lyapunov exponents for different system sizes. This data is analyzed using finite-size scaling to find the critical parameters. We create an energy-disorder phase diagram for both lattice types, noting that it is symmetric about the band center for the body centered cubic lattice, but not for the face centered cubic lattice. We find a critical exponent of approximately 1.5-1.6 for both lattice types for transitions occurring either at fixed energy or at fixed disorder, agreeing with results previously obtained for other systems belonging to the same orthogonal universality class. We notice an increase in critical disorder with the number of nearest neighbors, which agrees with intuition.
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