ABSENCE OF SELF-AVERAGING AND UNIVERSAL FLUCTUATIONS IN RANDOM-SYSTEMS NEAR-CRITICAL POINTS

The distributions P(X) of singular thermodynamic quantities, on an ens emble of d-dimensional quenched random samples of linear size L near a critical point, are analyzed using the renormalization group. For L m uch larger than the correlation length xi, we recover strong self-aver aging (SA): P(X) approaches a Gaussian with relative squared width R(X ) similar to (L/xi)(-d). For L much less than xi we show weak SA (R(X) decays with a small power of L) or no SA [P(X) approaches a non-Gauss ian, with universal L-independent relative cumulants], when the random ness is irrelevant or relevant, respectively.