Scaling up the Anderson transition in random-regular graphs

• URL: http://arxiv.org/abs/2005.13571v1
• Date: Wed, 27 May 2020 18:03:11 GMT
• Title: Scaling up the Anderson transition in random-regular graphs
• Authors: M. Pino
• Abstract summary: We study the Anderson transition in lattices with the connectivity of a random-regular graph. Our results indicate that fractal dimensions are continuous across the transition, but a discontinuity occurs in their derivatives. A critical exponent $nu = 1.00 pm0.02$ and critical disorder $W= 18.2pm 0.1$ are found via a scaling approach.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the Anderson transition in lattices with the connectivity of a random-regular graph. Our results indicate that fractal dimensions are continuous across the transition, but a discontinuity occurs in their derivatives, implying the non-ergodicity of the metal near the Anderson transition. A critical exponent $\nu = 1.00 \pm0.02$ and critical disorder $W= 18.2\pm 0.1$ are found via a scaling approach. Our data support that the predictions of the relevant Gaussian Ensemble are only recovered at zero disorder.

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