  The hope to realize Majorana fermions at the vortex core of a two dimensional
topological superconductor has led to a variety of proposals for devices which
exhibit topological superconductivity. Many of these include superconductivity
through the proximity effect and therefore require a layer of a conventional
superconductor deposited on top of another system, which lends its topological
properties\cite{Fu,Sau,Alicea}. The necessity of the superconducting layer
poses some technical complications and, in particular, makes it harder to probe
the Majorana state. In this work we propose to replace the proximity effect
pairing by an innate tendency for pairing, mediated by interactions. We use a
model system with spin orbit coupling and on-site repulsion and apply
renormalization group to the interaction vertex. Without a Zeeman field this
model exhibits pairing instabilities in different channels depending on the
tuning of parameters. Once a Zeeman field is introduced the model favors
topological superconductivity where the order parameter winds an odd number of
times around the Fermi surface. This suggests that certain superconductors,
with strong spin-orbit coupling, may go through a topological phase transition
as a function of applied magnetic field.
