I introduce a simple continuous probability theory based on the Ginzburg-Landau equation that provides a common analytical basis to relate and describe the main features of two seemingly different phenomena of condensed-matter physics, namely self-organized criticality and multifractality.

We compute the asymptotic structure factor S(k,t) of the O(n) model for n≤d, where d and n are the dimensions of space and of the order parameter, respectively. Topological defects in the field lead to the power-law tail S(k,t)=A(n,d)ρ(t)${\mathit{k}}^{\mathrm{-}(\mathit{d}+\mathit{n})}$, where ρ is the defect density. The amplitude A(n,d) is calculated exactly using purely geometrical arguments based on the defect field.