Renormalization flow of the hierarchical Anderson model at weak disorder
Renormalization flow of the hierarchical Anderson model at weak disorder
复制标题
弱无序情况下分层安德森模型的重正化流程
DOI：
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发表时间：
2013
期刊：
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通讯作者：
G. Parisi
中科院分区：
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作者：
F. L. Metz;L. Leuzzi;G. Parisi
我们研究了由一维Anderson模型的一系列简单变换得到的重整化模型参数的流动。将数值结果与流动方程的微扰方法相结合，我们发现在弱无序状态下存在三种性质不同的区域。对于足够快的跳跃能量衰减，柯西分布是流动方程中唯一稳定的不动点，而对于足够缓慢的跳跃能量衰减，重整化参数流动到一个三角峰不动点分布。在跳跃衰减的中间范围内，两个不动点分布都是稳定的，且平稳解由随机参数的初始构形决定。我们给出了区分不同区域的跳跃能量的临界衰变结果。
We study the flow of the renormalized model parameters obtained from a sequence of simple transformations of the 1D Anderson model with long-range hierarchical hopping. Combining numerical results with a perturbative approach for the flow equations, we identify three qualitatively different regimes at weak disorder. For a sufficiently fast decay of the hopping energy, the Cauchy distribution is the only stable fixed-point of the flow equations, whereas for sufficiently slowly decaying hopping energy the renormalized parameters flow to a delta peak fixed-point distribution. In an intermediate range of the hopping decay, both fixed-point distributions are stable and the stationary solution is determined by the initial configuration of the random parameters. We present results for the critical decay of the hopping energy separating the different regimes.