  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.
