Finite-Size Scaling and Lack of Self-Averaging in Critical Disordered Systems

We simulated site dilute Ising models in d0ex0ex=0ex0ex3 dimensions for several lattice sizes L. For each L singular thermodynamic quantities X were measured at criticality and their distributions $P(X)$ were determined for ensembles of several thousand random samples. For L→∞ the relative width of $P(X)$ tends to a universal constant: there is no self-averaging. The width of the distribution of the sample $(i)$ dependent pseudocritical temperatures Tc(i,L) scales as δTc(L)~L^-1/ν and not as ~L^-d/2. The sample dependence of Xᵢ(T,L) enters dominantly, but not exclusively, via Tc(i,L).