F. Pazmandi et al., REVISITING THE THEORY OF FINITE-SIZE-SCALING IN DISORDERED-SYSTEMS - NU CAN BE LESS-THAN 2 D/, Physical review letters, 79(25), 1997, pp. 5130-5133
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.