A numerical method is developed to study the scaling of distribution of couplings of highly random antiferromagnetic Ising and quantum Heisenberg spin-½ systems. The method shows how freezing into inert local singlets prevents ordering down to temperatures well below the median nearest-neighbor coupling or bare exchange percolation threshold in positionally disordered systems with Heisenberg exchange varying exponentially with distance (e.g., doped semiconductors, quasi one-dimensional salts). This is contrasted with the Ising system.

• Received 6 May 1981

DOI:https://doi.org/10.1103/PhysRevLett.48.344