Effects of instability of quantum critical behaviour in systems with quenched impurities

The one-loop renormalization group equations are derived and analysed for a wide class of quantum statistical models describing the critical behaviour of systems with short-range correlated random impurities. The classical and quantum critical properties are considered to first order in a double ε-expansion. It is proven that the quantum critical behaviour of disordered systems with short-range random correlation is equivalent to the classical critical behaviour of certain systems with extended random impurities. The reliability of the double ε-expansion method and the interpretation of the results are discussed.