Model for a random-matrix description of the energy-level statistics of disordered systems at the Anderson transition

We consider a family of random-matrix ensembles (RME's) invariant under similarity transformations and described by the probability density P(H)=exp[-TrV(H)]. Dyson's mean-field theory (MFT) of the corresponding plasma model of eigenvalues is generalized to the case of weak confining potential, V(epsilon)similar to(A/2)ln(2)(epsilon). The eigenvalue statistics derived from MFT are shown to deviate substantially from the classical Wigner-Dyson statistics when A<1. By performing systematic Monte Carlo simulations on the plasma model, we compute all the relevant statistical properties of the RME's with weak confinement. For A(c) approximate to 0.4 the distribution function of the energy-level spacings (LSDF) of this RME coincides in a large energy window with the LSDF of the three-dimensional Anderson model at the metal-insulator transition. For the same A(c), the variance of the number of levels, (n(2))-(n)(2), in an interval containing (n) levels on average, grows linearly with (n), and its slope is equal to 0.32+/-0.02, which is consistent with the value found for the Anderson model at the critical point.