Abstract
Then-orbital gauge-invariant model of disordered electronic systems proposed by Wegner is studied in the regime of dominant diagonal disorder. Analyticity of the density of states is established in two cases: (a) when the number of orbitals is small, (b) when the number of orbitals is large and the energy is in the expected extended states region.
Similar content being viewed by others
References
D. J. Thouless,Introduction to Disordered Systems (Les Houches Lectures XLIII, Elsevier, 1986).
T. Spencer,The Schrödinger Equation with Random Potential (Les Houches Lectures XLIII, Elsevier, 1986).
F. Delyon and B. Souillard,Commun. Math. Phys. 94:289–291 (1984).
F. Wegner,Phys. Rev. B 19:783–792 (1979).
F. Wegner,Phys. Rep. 67:15–24 (1980).
L. Schäfer and F. Wegner,Z. Phys. B Condensed Matter 38:113–126 (1980).
K. B. Efetov,Adv. Phys. 32:53–127 (1983).
F. Delyon, B. Simon, and B. Souillard, Localization for off-diagonal disorder and for continuous Schrödinger operators, preprint (1986).
K. Ziegler,Z. Phys. B Condensed Matter 48:293–304 (1982); Analytic averaged density of states of a tight binding model with disorder, Preprint 241, Sonderforschungsbereich 123, Universität Heidelberg (1983), unpublished.
F. Constantinescu, J. Fröhlich, and T. Spencer,J. Stat. Phys. 34:571–596 (1984).
E. P. Wigner,Ann. Math. 62:548 (1955);67:325 (1958).
F. Wegner,Z. Physik B 44:9–15 (1981).
R. Oppermann and F. Wegner,Z. Phys. B 34:327–348 (1979).
J. Glimm and A. Jaffe,Quantum Physics (Springer-Verlag, New York, 1981), Part III, §18.
K. Jügling and R. Oppermann,Z. Phys. B 38:93 (1980).
J. Glimm, A. Jaffe, and T. Spencer,Ann. Phys. (N.Y.) 101:610–630, 631–669 (1976).
T. Balaban and K. Gawedzki,Ann. Inst. Henri Poincaré 34:271–400 (1982).
F. Constantinescu and B. Ströter,J. Math. Phys. 21:881–891 (1980).
K. Klöckner and B. Ströter,Commun. Math. Phys. 86:495–508 (1982).
G. Gallavotti, A. Martin-Löf, and S. Miracle-Sole, inStatistical Mechanics and Mathematical Problems (Springer, Berlin, 1973).
E. Seiler,Gauge Theories As a Problem of Constructive Quantum Field Theory and Statistical Mechanics (Springer, Berlin, 1982).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Constantinescu, F., Felder, G., Gawedzki, K. et al. Analyticity of density of states in a gauge-invariant model for disordered electronic systems. J Stat Phys 48, 365–391 (1987). https://doi.org/10.1007/BF01019679
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01019679