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We apply the fermion renormalization group method, implemented numerically byHonerkamp et.al., to a two-band model of FeAs-based materials. At half fillingwe find the $(\pi,0)$ or $(0,\pi)$ spin density wave order and a sub-dominantsuperconducting pairing tendency. Due to a topological reason, the spin densitywave gap has nodes on the fermi surfaces. Away from half filling we find anunconventional s-wave and a sub-dominant $d_{x^2-y^2}$ pairing instability. Theformer has $s$ symmetry around the hole fermi surface but exhibits$s+d_{x^2-y^2}$ symmetry around the electron pockets where the 90 degreerotation is broken. The pairing mechanism is inter-pocket pair hopping.Interestingly, the same interaction also drives the antiferromagnetism.

A Numerical Renormalization Group Study of the Superconducting and Spin Density Wave Instabilities in MFeAsO$_{1-x}$F$_x$ Compounds