Zeitschrift für Physik B Condensed Matter

, Volume 51, Issue 4, pp 279–285 | Cite as

Exact density of states for lowest Landau level in white noise potential superfield representation for interacting systems

  • Franz Wegner


The density of states of two-dimensional electrons in a strong perpendicular magnetic field and white-noise potential is calculated exactly under the provision that only the states of the free electrons in the lowest Landau level are taken into account. It is used that the integral over the coordinates in the plane perpendicular to the magnetic field in a Feynman graph yields the inverse of the number λ of Euler trails through the graph, whereas the weight by which a Feynman graph contributes in this disordered system is λ times that of the corresponding interacting system. Thus the factors λ cancel which allows the reduction of thed dimensional disordered problem to a (d-2) dimensional φ4 interaction problem. The inverse procedure and the equivalence of disordered harmonic systems with interacting systems of superfields is used to give a mapping of interacting systems withU(1) invariance ind dimensions to interacting systems with UPL(1,1) invariance in (d+2) dimensions. The partition function of the new systems is unity so that systems with quenched disorder can be treated by averaging exp(−H) without recourse to the replica trick.


Magnetic Field Neural Network Partition Function White Noise Nonlinear Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Franz Wegner
    • 1
  1. 1.Institut für Theoretische PhysikRuprecht-Karls-UniversitätHeidelbergFederal Republic of Germany

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