PERCOLATION AND CONDUCTION
PERCOLATION AND CONDUCTION
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DOI：
10.1103/revmodphys.45.574
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发表时间：
1973-01-01
影响因子：
44.1
通讯作者：
KIRKPATRICK, S
中科院分区：
文献类型：
--
作者：
KIRKPATRICK, S
描述了渗流理论在处理输运问题上的扩展。随机移除电阻的电阻网络提供了先前考虑过渗流阈值和渗流概率的晶格模型的自然推广。证明了这种网络的归一化电导G是一个严格定义的量，在阈值附近有一个特征的浓度依赖关系，它似乎只对维度敏感。给出了几类三维和二维网络模型的数值结果。除了接近阈值外，基于键渗流的模型都可以用一个简单的有效介质理论来精确描述，它也可以处理连续介质或不像渗流模型那样剧烈的情况，例如局部电导率具有连续分布的材料。目前的计算首次对这一理论进行了定量检验。给出了有效介质理论的“格林函数”推导，它使无序合金的类似处理发生了接触。最后，得到了渗流模型电导的一般表达式，它将G与适当定义的稀铁磁体模型的自旋刚度系数D联系起来。我们利用这个关系来论证，电流在阈值以上流动的“渗流通道”必须被视为三维的。
Extensions of percolation theory to treat transport are described. Resistor networks, from which resistors are removed at random, provide the natural generalization of the lattice models for which percolation thresholds and percolation probabilities have previously been considered. The normalized conductance, G, of such networks proves to be a sharply defined quantity with a characteristic concentration dependence near threshold which appears sensitive only to dimensionality. Numerical results are presented for several families of 3 D and 2 D network models. Except close to threshold, the models based on bond percolation are accurately described by a simple effective medium theory, which can also treat continuous media or situations less drastic than the percolation models, for example, materials in which local conductivity has a continuous distribution of values. The present calculations provide the first quantitative test of this theory. A" Green's function" derivation of the effective medium theory, which makes contact with similar treatments of disordered alloys, is presented. Finally, a general expression for the conductance of a percolation model is obtained which relates G to the spin-stiffness coefficient, D, of an appropriately defined model dilute ferromagnet. We use this relationship to argue that the" percolation channels" through which the current flows above threshold must be regarded as three dimensional.