Séminaire du LPTMS: Vladimir Kravtsov *** séminaire exceptionnel ***


11:00 - 12:00

LPTMS, salle 201, 2ème étage, Bât 100, Campus d'Orsay
15 Rue Georges Clemenceau, Orsay, 91405

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Phases and phase transitions on disordered Bethe lattice: analytical treatment by one-step replica symmetry breaking

Vladimir Kravtsov (ICTP, Trieste, Italy)

We apply the replica trick to the problem of localization on disordered  Bethe lattice. We show that the formulation of the problem in terms of  the one-step replica symmetry breaking leads naturally to existence of  the multifractal phase and to phase transitions between this phase and  the localized and fully extended (ergodic) delocalized phase. We prove  the symmetry m→1-m of the problem with respect to the replica symmetry  breaking parameter m and use this symmetry to derive exact expressions  for the transition points in terms of the Lyapuniov exponents and the  branching number K. We also suggest a simple approximation which allows  to compute the fractal dimension D1 in the multifractal phase and the  critical values of disorder at the phase transitions with the best known  so far accuracy.

Reference :

  • B. L. Altshuler, L. B. Ioffe and V. E. Kravtsov, Multifractal states in self-consistent theory of localization: analytical solution, preprint arXiv:1610.00758
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