Scaling Studies of Highly Disordered Spin-½ Antiferromagnetic Systems
A numerical method is developed to study the scaling of distribution of couplings of highly random antiferromagnetic Ising and quantum Heisenberg spin-\textonehalf{} 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.