A critical Dyson hierarchical model for the Anderson localization transition

DOI10.1088/1742-5468/2011/05/P05005zbMath1456.82518arXiv1102.4701OpenAlexW2080438490MaRDI QIDQ3301248

Thomas Garel, Cécile Monthus

Publication date: 11 August 2020

Published in: Journal of Statistical Mechanics: Theory and Experiment (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1102.4701

Mathematics Subject Classification ID

Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Critical phenomena in equilibrium statistical mechanics (82B27)

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Cites Work

• Unnamed Item
• Poisson statistics of eigenvalues in the hierarchical Anderson model
• Critical phenomena and universal exponents in statistical physics. On Dyson's hierarchical model
• Existence of a phase-transition in a one-dimensional Ising ferromagnet
• The density of states in the Anderson model at weak disorder: A renormalization group analysis of the hierarchical model
• Critical Hamiltonians with long range hopping
• Anderson localization on the Cayley tree: multifractal statistics of the transmission at criticality and off criticality
• Random elastic networks: a strong disorder renormalization approach
• The Anderson localization transition with long-ranged hoppings: analysis of the strong multifractality regime in terms of weighted Lévy sums
• Spectral localization in the hierarchical Anderson model
• Virial expansion for almost diagonal random matrices
• The Anderson localization transition and eigenfunction multifractality in an ensemble of ultrametric random matrices
• A supersymmetry approach to almost diagonal random matrices
• Supersymmetric virial expansion for time-reversal invariant disordered systems
• Level compressibility in a critical random matrix ensemble: the second virial coefficient
• Renormalization group and probability theory