Multifractal finite-size scaling and universality at the Anderson transition
Multifractal finite-size scaling and universality at the Anderson transition
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DOI：
10.1103/physrevb.84.134209
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发表时间：
2011-10-31
影响因子：
3.7
通讯作者：
Roemer, Rudolf A.
中科院分区：
文献类型：
--
作者：
Rodriguez, Alberto;Vasquez, Louella J.;Roemer, Rudolf A.
我们描述了一种新的多重分形有限尺度方法及其在安德森定域-离域跃迁中的应用。MFSS允许的临界参数和多重分形指数的同时估计。对L ~（-3）= 120（3）的系统进行了模拟，得到了临界无序W-c = 16.530（16.524，16.536）和临界指数nu = 1.590（1.579，1.602）的空前精确的结果。我们发现，多重分形指数λ（q）表现出先前预测的对称关系，我们确认其频谱的非抛物性质。我们详细解释了MFSS程序首先介绍了我们的信[物理学。105，046403（2010）]，此外，我们还展示了如何考虑模拟数据中的相关性。MFSS程序适用于在临界点附近表现出多重分形波动的任何连续相变。
We describe a new multifractal finite-size scaling (MFSS) procedure and its application to the Anderson localization-delocalization transition. MFSS permits the simultaneous estimation of the critical parameters and the multifractal exponents. Simulations of system sizes up to L-3 = 120(3) and involving nearly 10(6) independent wave functions have yielded unprecedented precision for the critical disorder W-c = 16.530(16.524,16.536) and the critical exponent nu = 1.590(1.579,1.602). We find that the multifractal exponents Lambda(q) exhibit a previously predicted symmetry relation and we confirm the nonparabolic nature of their spectrum. We explain in detail the MFSS procedure first introduced in our Letter [Phys. Rev. Lett. 105, 046403 (2010)] and, in addition, we show how to take account of correlations in the simulation data. The MFSS procedure is applicable to any continuous phase transition exhibiting multifractal fluctuations in the vicinity of the critical point.