无自相似的临界性：具有随机长程跳变的2D系统
Criticality without self-similarity: a 2D system with random long-range hopping
摘要：
我们考虑一个简单的二维量子无序模型，其特征在于一个长距离的网站到网站的跳跃。该系统经历了一个金属-绝缘体转变-其本征函数从被扩展到被本地化的变化。我们证明，在过渡点的特征函数不成为分形。它们的密度矩不随系统大小的幂而变化。相反，在一个考虑的限制，我们的结果表明，幂的对数的系统大小。在这方面，过渡不同于类似的一个在一维版本的同一系统，以及从传统的安德森过渡在两个以上的维度。
英文摘要：
We consider a simple model of quantum disorder in two dimensions, characterized by a long-range site-to-site hopping. The system undergoes a metal-insulator transition -- its eigenfunctions change from being extended to being localized. We demonstrate that at the point of the transition the eigenfunctions do not become fractal. Their density moments do not scale as a power of the system size. Instead, in one of the considered limits our result suggests a power of the logarithm of the system size. In this regard, the transition differs from a similar one in the one-dimensional version of the same system, as well as from the conventional Anderson transition in more than two dimensions.
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