We study the Anderson transition in lattices with the connectivity of a random-regular graph. Our results show that fractal dimensions are continuous across the transition, but a discontinuity occurs in their derivatives, implying the existence of a nonergodic metallic phase with multifractal eigenstates. The scaling analysis gives critical exponent $\nu =0.94\pm 0.08$ and critical disorder $W_{\mathrm{c}}=18.17\pm 0.02.$ Our data support that ergodicity is only recovered at zero disorder.

中文翻译：

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扩大随机正则图中的Anderson转换

我们研究了具有随机规则图的连通性的格子中的安德森过渡。我们的结果表明，分形维数在过渡过程中是连续的，但它们的导数不连续，这表明存在具有多重分形本征态的非遍历金属相。缩放分析给出了关键指数$\nu =0.94\pm 0.08$ 和重症 ${\mathrm{w\; ^}}_{\mathrm{C}}=18.17\pm 0.02。$ 我们的数据支持遍历性仅在零失调时才能恢复。