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Long range magnetic ordering in the quasi-one-dimensional random-bondantiferromagnet BaCu$_2$(Si$_{1-x}$Ge$_{x}$)$_2$O$_7$ is studied in $\mu$SRexperiments as a function of disorder strength. Compared to the disorder-freeparent materials, the saturation ordered moment is found to be considerablyreduced. Moreover, even in weakly disordered species, the magnetically orderedstate is shown to be highly inhomogeneous. The results are interpreted in termsof weakly coupled random spin chains, governed by the ``infinite randomness``fixed point.

Inhomogeneous ordering in weakly coupled Heisenberg $S=1/2$ chains with random bonds