Multifractality-monofractality phase transition in the Anderson model

It is shown that statistics of multifractality-monofractality phase transition is described by a generalization of the Bernoulli distribution (multifractal Bernoulli distribution). It is also shown that this distribution is observed in numerical simulations of multifractal wave functions which use the Anderson model, both for short- and long-range disorder. In the last case (corresponding to the dipole interactions) the multifractal specific heat of the most eigenstates - c similar or equal to d/3, where d is dimension of the space.