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The ground state of the quasi-one-dimensional system with bond-disorder(CH3)2CHNH3Cu(ClxBr1-x)3 with x = 0, 0.25 and 0.3 has been investigated bymuSR. The Fourier spectrum of electron spin fluctuation in x =0.25 and 0.3obtained by LF-muSR technique shows that there exists a soft-mode toward apossible phase transition to an exotic phase such as Bose-glass. In gappedsystem with x = 0, the Fourier spectrum is totally different from the othertwo, indicating the existence of the quantum critical point at a finite xbetween 0 and 0.25.

Ground state of bond-disordered quasi-one-dimensional spin system (CH3)2CHNH3Cu(ClxBr1-x)3 with x = 0, 0.25 and 0.3