  We present a detailed analysis of the non-analytic structure of the free
energy for the itinerant ferromagnet near the quantum critical point in two and
three dimensions. We analyze a model of electrons with an isotropic dispersion
interacting through a contact repulsion. A fermionic version of the quantum
order-by-disorder mechanism allows us to calculate the free energy as a
functional of the dispersion in the presence of homogeneous and spiralling
magnetic order. We re-sum the leading divergent contributions, to derive an
algebraic expression for the non-analytic contribution to free energy from
quantum fluctuations. Using a recursion which relates sub-leading divergences
to the leading term, we calculate the full T=0 contribution in $d=3$. We
propose an interpolating functional form, which allows us to track phase
transition lines at temperatures far below the tricritical point and down to
T=0. In $d=2$, quantum fluctuations are stronger and non-analyticities more
severe. Using a similar re-summation approach, we find that despite the
different non-analytic structures, the phase diagrams in two and three
dimensions are remarkably similar, exhibiting an incommensurate spiral phase
near to the avoided quantum critical point.
