  The nonperturbative phenomena of QCD like color confinement is well described
through the dual superconductor picture in the Maximally Abelian (MA) gauge. In
this gauge, monopoles appear as important degrees of freedom composed by
nonabelian gauge fields. We investigate the peculiar size $R_c$ of the monopole
in the MA gauge, considering the theoretical similarity between spinglass and
the MA gauge fixing. As for the properties at larger scale than the monopole
size $R_c$, the system can be described by the dual superconductor theory with
local abelian fields. At shorter distances than $R_c$, such a dual Higgs theory
should be treated as a non-local field theory, and therefore one must take
another framework like the perturbative QCD. Thus, the monopole size gives a
critical scale on the change of the theoretical structure of QCD.
