Level number variance and spectral compressibility in a critical   two-dimensional random matrix model
  We study level number variance in a two-dimensional random matrix model characterized by a power-law decay of the matrix elements. The amplitude of the decay is controlled by the parameter b. We find analytically that at small values of b the level number variance behaves linearly, with the compressibility chi between 0 and 1, which is typical for critical systems. For large values of b, we derive that chi=0, as one would normally expect in the metallic phase. Using numerical simulations we determine the critical value of b at which the transition between these two phases occurs. 
A. Ossipov, I. Rushkin, E. Cuevas
cond-mat.dis-nn cond-mat.stat-mech math-ph math.MP