Two-dimensional random-bond Ising model, free fermions, and the network model
Two-dimensional random-bond Ising model, free fermions, and the network model
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二维随机键伊辛模型、自由费米子和网络模型
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
J. Chalker
中科院分区：
文献类型：
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作者：
F. Merz;J. Chalker
我们发展了最近提出的具有随机交换的二维伊辛模型(RBIM)通过传输矩阵到非相互作用费米子无序系统的网络模型的映射。RBIM以这种方式转化为属于一组非标准对称类中的一个的局域化问题，称为D类；顺磁和铁磁之间的转变等价于绝缘体和量子霍尔导体之间的离域转变。我们将这种映射建立为一种精确而有效的数值分析工具：使用它，研究一个宽度为M的系统所需的计算量与${M}^{3}成正比，而不是像传统算法那样在M中呈指数关系。我们展示了如何使用这种方法来计算RBIM的自由能，自旋和无序算符在准一维中的典型关联长度，以及自旋-自旋关联函数及其无序平均值的偶次幂。我们详细地研究了正方形晶格，最近邻的$ifmmodesmse extpmfi{}J$rBIM，其中键以概率p独立地反铁磁性，以概率$1确保为铁磁性。研究温度$Tg~0.4J，我们得到了铁磁和顺磁之间的相界点和多临界(Nishimori)点在T平面上的精确坐标。我们证明了在小p处向纯Ising不动点的标度流，并确定了多临界点的临界指数。
We develop a recently proposed mapping of the two-dimensional Ising model with random exchange (RBIM) via the transfer matrix, to a network model for a disordered system of noninteracting fermions. The RBIM transforms in this way to a localization problem belonging to one of a set of nonstandard symmetry classes, known as class D; the transition between paramagnet and ferromagnet is equivalent to a delocalization transition between an insulator and a quantum Hall conductor. We establish the mapping as an exact and efficient tool for numerical analysis: using it, the computational effort required to study a system of width M is proportional to ${M}^{3},$ and not exponential in M as with conventional algorithms. We show how the approach may be used to calculate for the RBIM the free energy, typical correlation lengths in quasi-one dimension for both the spin and the disorder operators, and the even powers of spin-spin correlation functions and their disorder averages. We examine in detail the square-lattice, nearest-neighbor $ifmmodepmelse extpmfi{}J$ RBIM, in which bonds are independently antiferromagnetic with probability p, and ferromagnetic with probability $1ensuremath{-}p.$ Studying temperatures $Tg~0.4J,$ we obtain precise coordinates in the $pensuremath{-}T$ plane for points on the phase boundary between ferromagnet and paramagnet, and for the multicritical (Nishimori) point. We demonstrate scaling flow towards the pure Ising fixed point at small p, and determine critical exponents at the multicritical point.