Analyticity of the density of states and replica method for random Schrödinger operators on a lattice. (English) Zbl 0591.60060

Constantinescu, F.; Fröhlich, J.; Spencer, T.

J. Stat. Phys. 34, 571-596 (1984).

Summary: We analyze the density of states and some aspects of the replica method for Anderson’s tight binding model on a lattice of arbitrary dimension, with diagonal disorder. We give heuristic arguments for the conjectures that the classical value of the exponent v of the localization length is 1/2 and that the upper critical dimension, \(d_ c^{loc}\), is bounded by \(4\leq d_ c^{loc}\leq 6\).

MSC:

60H25	Random operators and equations (aspects of stochastic analysis)
60K35	Interacting random processes; statistical mechanics type models; percolation theory

Keywords:

random Schrödinger operators on a lattice; tight binding model; replica method; density of states

References:

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