REVISITING THE THEORY OF FINITE-SIZE-SCALING IN DISORDERED-SYSTEMS - NU CAN BE LESS-THAN 2 D/

For phase transitions in disordered systems, an exact theorem provides a bound on the finite size correlation length exponent: nu(FS) greate r than or equal to 2/d. it is believed that the intrinsic nu satisfies the same bound. We argue that the standard averaging introduces a noi se and a new diverging length scale. For nu less than or equal to 2/d self-averaging breaks down, disconnecting nu from nu(FS), and the boun d applies only for the latter. We illustrate these ideas on two exact examples, with nu < 2/d. We propose a new method of disorder averaging , which is able to capture the intrinsic exponents.