We examine the effect of classical magnetic fluctuations on the phase diagram
of paramagneticallylimited two-dimensional superconductors under a Zeeman
magnetic field. We derive the free energy expansion in powers of the
superconducting order parameter and analyze the character of the
normalsuperconducting transition. While the transition is of the second order
for all temperatures in the absence of magnetic fluctuations, we find that
proximity to magnetism drives both the transition into the uniform state and
that into the modulated (Fulde-Ferrell-Larkin-Ovchinnikov, FFLO) state to first
order at intermediate temperatures. We compute the thermodynamic signatures of
the normal-superconducting transition along the upper critical field.Comment: 16 pages, 9 figure