  We show that two-band superconductors harbor hidden criticality deep in the
superconducting state, stemming from the critical temperature of the weaker
band taken as an independent system. For sufficiently small interband coupling
$\gamma$ the coherence length of the weaker band exhibits a remarkable
deviation from the conventional monotonic increase with temperature, namely, a
pronounced peak close to the hidden critical point. The magnitude of the peak
scales proportionally to \gamma^(-\mu), with the Landau critical exponent \mu =
1/3, the same as found for the mean-field critical behavior with respect to the
source field in ferromagnets and ferroelectrics. Here reported hidden
criticality of multi-band superconductors can be experimentally observed by,
e.g., imaging of the variations of the vortex core in a broader temperature
range. Similar effects are expected for the superconducting multilayers.
