Thermodynamics of diluteXYquantum chains

It is shown that the specific heat and susceptibility (${\chi }^{\mathrm{zz}}$) of the dilute $\mathrm{XY}$ $\mathrm{s}\mathrm{p}\mathrm{i}\mathrm{n}-\frac{1}{2}$ chain can be calculated by summing over the finite segments. At low temperatures the specific heat is determined by segments with an even number of spins, whereas the susceptibility is determined by segments with an odd number of spins. At low temperatures the specific heat behaves as ${\left(\frac{T_0}{T}\right)}^{\frac{5}{4}}\exp [-2\mathrm{}{\left(\frac{T_0}{T}\right)}^{\frac{1}{2}}]$, where $T_0$ is a characteristic temperature in the dilute spin system.