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It is argued that the phase transition in low-T_c clean itinerantferromagnets is generically of first order, due to correlation effects thatlead to a nonanalytic term in the free energy. A tricritical point separatesthe line of first order transitions from Heisenberg critical behavior at highertemperatures. Sufficiently strong quenched disorder suppresses the first ordertransition via the appearance of a critical endpoint. A semi-quantitativediscussion is given in terms of recent experiments on MnSi and UGe_2. It isthen shown that the critical temperature for spin-triplet, p-wavesuperconductivity mediated by spin fluctuations is generically much higher in aHeisenberg ferromagnetic phase than in a paramagnetic one, due to the couplingof magnons to the longitudinal magnetic susceptibility. This qualitativelyexplains the phase diagram recently observed in UGe_2 and ZrZn_2.Comment: 10 pp., LaTeX, 5 ps figs., requires World Scientific style files  (included), Invited contribution to MB1

SUPERCONDUCTIVITY AND QUANTUM PHASE TRANSITIONS IN WEAK ITINERANT FERROMAGNETS