The thermodynamic properties of a soliton-bearing system without translation invariance---the dilute
S=21 anisotropic
XY chain---are calculated. At low temperatures the dominant contribution comes from a low-energy complex mode, which assumes zero energy when translational symmetry is restored in the pure system. The density of states of the complex modes is found to exhibit a scaling property with a fractional spectral dimensionality $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{d}=\frac{2\mathrm{ln}c}{\mathrm{ln}\ensuremath{\lambda}}$, with
c the concentration of magnetic sites and $\ensuremath{\lambda}$ related to the anisotropy. Consequently, the specific heat shows the anomalous behavior $C(T)\ensuremath{\propto}{T}^{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{d}}$.
We use a pseudofermion representation to investigate strong-field anomalies of the magnetic-field (h) dependence of the specific heat (c) of a spin-1/2 XY chain doped with magnetic impurities. If at certain magnetic field the impurity-induced split-off energy levels come sufficiently close to the chemical potential of pseudofermions (zero), then at low temperatures the specific heat of the chain is significantly altered by even a small number of impurities. The impurity-induced peaks of the c(h) dependence correspond to magnetic fields in a range where the specific heat of the ideal spin-1/2 XY chains is exponentially small. They have the same physical origin, but different structure, as compared to the high-field anomalies of longitudinal magnetic susceptibility investigated previously.