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Accueil du site > Séminaires > Séminaires 2019 > Critical Exponent of the Anderson Transition using Massively Parallel Supercomputing

Mardi 11 juin 2019 - 14:00

Critical Exponent of the Anderson Transition using Massively Parallel Supercomputing

Keith Slevin, Université d’Osaka (Japon)

par Revaz Ramazashvili - 11 juin 2019

To date the most precise estimations of the critical exponent for the Anderson transition have been made using the transfer matrix method introduced into the field of Anderson localization by Pichard and Sarma [1], and MacKinnon and Kramer [2]. This method involves the simulation of extremely long quasi one-dimensional systems. The method is inherently sequential and is not well suited to modern massively parallel supercomputers. The obvious alternative is to simulate a large ensemble of hypercubic systems and average. While this makes it possible to take full advantage of both OpenMP and MPI on massively parallel supercomputers, a straightforward implementation results in data that does not scale. We show that this problem can be avoided by generating random sets of orthogonal initial vectors with an appropriate stationary probability distribution. We have applied this method to the Anderson transition in the three-dimensional orthogonal universality class and been able to increase the largest L × L cross section simulated from L=24 in [3] to L=64 [4]. Using this method, we have estimated the critical exponent with improved precision, and without the necessity of introducing an irrelevant scaling variable.

1. Pichard, J.L. and G. Sarma, Finite size scaling approach to Anderson localisation. Journal of Physics C : Solid State Physics, 14(6), L127 (1981).

2. MacKinnon, A. and B. Kramer, One-parameter scaling of localization length and conductance in disordered systems. Physical Review Letters, 47(21), 1546 (1981).

3. Slevin, K. and T. Ohtsuki, Critical exponent for the Anderson transition in the three-dimensional orthogonal universality class. New Journal of Physics, 16(1), 015012 (2014).

4. Slevin, K. and T. Ohtsuki, Critical Exponent of the Anderson Transition Using Massively Parallel Supercomputing. Journal of the Physical Society of Japan, 87(9), 094703 (2018).

Post-scriptum :

contact : G. Lemarié