  We compare the phase-diagrams of an effective theory of a three-dimensional
multi-band superconductor obtained within standard and cluster mean-field
theories, and in large-scale Monte Carlo simulations. In three dimensions, mean
field theory fails in locating correctly the positions of the phase
transitions, as well as the character of the transitions between the different
states. A cluster mean-field calculations taking into account order-parameter
fluctuations in a local environment improves the results considerably for the
case of extreme type-II superconductors where gauge-field fluctuations are
negligible. The large fluctuations in the multi-component superconducting order
parameter originate with strong frustration due to interband
Josephson-couplings. A novel chiral metallic phase found in previous works
using large scale Monte-Carlo computations, is not obtained either within the
single-site mean-field theory or the improved cluster mean-field theory of
order parameter fluctuations. In three-dimensional superconductors, this
unusual metallic phase originates with gauge-field fluctuations.
