title: Level-number variance and spectral compressibility in a critical two-dimensional random-matrix model.
abstract: 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 χ between 0 and 1, which is typical for critical systems. For large values of b, we derive that χ=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.
authors.affiliation: School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom.
authors.forename: A
authors.initials: A
authors.lastname: Ossipov
authors.forename: I
authors.initials: I
authors.lastname: Rushkin
authors.forename: E
authors.initials: E
authors.lastname: Cuevas
mesh_terms: D003198:Computer Simulation; D008956:Models, Chemical; D008958:Models, Molecular; D044367:Phase Transition