“…This leads to random walks, with a nonvanishing occurrence of long jumps [3][4][5] , as well as long-range ordering effects in organic and inorganic materials 2,[6][7][8][9] . Spin-1/2 chains with antiferromagnetic interaction, so called the spinPeierls systems 10,11 , as well as cross-coupled spin-1/2 chains, so called the spin-ladder systems 12,13 , are both prime examples of solids with long-range ordered phases. Doping in these materials causes impurity spins, which support low-energy, exponentially localized defect states within the band gap of the host material, but exhibit long-range averaged correlations decaying with a power law over distance.…”