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A model of disordered spin-Peierls system is considered, where domain wallsare randomly distributed as a telegraph noise. For this realization of thedisorder in an XX spin chain, we calculate exactly the density of states aswell as several thermodynamic quantities. The resulting physical behaviorshould be qualitatively unchanged even for an XXZ chain, up to the isotropicXXX point. For weak disorder, besides a high energy regime where the behaviorof a pure spin-Peierls system is recovered, there is a cross-over to a lowenergy regime with singular thermodynamic properties and enhancedantiferromagnetic fluctuations. These regimes are analyzed with the help ofexact results, and the relevant energy scales determined. We discuss thepossible relevance of such a disorder realization to the doped inorganicspin-Peierls compound CuGeO$_3$.Comment: 4 pages, 2 included figure

Coexistence of Antiferromagnetism and Dimerization in a Disordered Spin-Peierls Model: Exact Results