Quantum Hall transition in an array of quantum dots

A two-dimensional array of quantum dots in a magnetic field is considered. The electrons in the quantum dots are described as unitary random matrix ensembles. The strength of the magnetic field is such that there is half a flux quantum per plaquette. This model exhibits the integer quantum Hall effect. For N electronic states per quantum dot the limit N→∞ can be solved by a saddle-point integration of a supersymmetric field theory. The effect of level statistics on the density of states and the Hall conductivity is compared with the effect of temperature fluctuations.