Magnetic susceptibility of disordered one-dimensional systems

The magnetic susceptibility of various one-dimensional (1-D) disordered models is studied. At low temperatures and small transfer integrals the Hubbard model reduces to that of a disordered 1-D Heisenberg antiferromagnet with probability distribution of exchange of the form P(J)∝1J^1-c. Via a cluster argument we find that the low-temperature magnetic susceptibility behaves as χ∝1T^1-c. That is, it has a singularity at $T=0$^∘{}K of the same form as that of the probability distribution. Various exactly soluble model Hamiltonians were also studied using the same probability distribution. From these studies we have inferred that for a sufficiently disordered system the quantum 1-D Heisenberg model can be adequately represented by the classical Heisenberg model.