Random Exchange Heisenberg Chain for Classical and Quantum Spins

The Heisenberg chain with random $\pm J$ bonds is studied for the quantum spin $s=\frac{1}{2}$ and in the classical limit. The former is treated by high-temperature expansion and transfer matrix calculation while the latter can be analyzed exactly. The disorder leads to a $\frac{1}{T}$ behavior of the low-temperature susceptibility in the classical system. For $s=\frac{1}{2}$ our analysis reveals a significant residual entropy at low temperature. From this we conclude that for quantum spins the susceptibility exhibits three different regimes in temperature and that the specific heat has a peak in the very low-temperature regime.