The results of high frequency (60-315 GHz) studies of the ESR in CuGeO3 single crystals containing 0.9% of the Mn impurity are reported. The quantitative ESR line shape analysis shows that the low temperature (T<40 K) magnetic susceptibility of Cu2+ chains diverges with the critical exponent a=0.81 and therefore indicates an onset of a quantum critical (QC) regime. The scenario, in which disorder caused by the Mn impurity in the quantum spin chains in CuGeO3 may lead to the co-existence of the QC regime and the spin-Peierls dimerisation, is discussed. For the quantitative description of the temperature dependences of the line width and g-factor a model assuming the crossover from the high temperature semiclassical Nagata and Tazuke limit to the low temperature quantum case described by Oshikawa and Affleck theory is suggested.
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