  We solve the problem of fermionic pairing mediated by a massless boson in the
limit of large coupling constant. At weak coupling, the transition temperature
is exponentially small and superconductivity is robust against phase
fluctuation. In the strong coupling limit, the pair formation occurs at a
temperature of the order of the Fermi energy, however, the actual transition
temperature is much smaller due to phase and amplitude fluctuations of the
pairing gap.
  Our model calculations describe superconductivity due to color magnetic
interactions in quark matter and in systems close to a ferromagnetic quantum
critical point with Ising symmetry. Our strong coupling results are, however,
more general and can be applied to other systems as well, including the
antiferromagnetic exchange in 2D used for description of the cuprates.
