  In this work we investigate the scaling properties of quasiparticles of
Pnictide with "half-Dirac" node under magnetic field in vortex state. By
computing the density of states, we aim to find in vortex state the form of
non-Simon-Lee scaling predicted for such system by several recent works in
non-vortex state. We find by exact diagonalization of the Bogoliubov-de Genne
Hamiltonian and finite size scaling a $N(E)\sim \sqrt{E}$ power law in the case
without magnetic field which agrees with analytical prediction. We consider the
vortex state by first studying the hypothetical situation of uniform magnetic
field without vortices and then we properly treat the magnetic field-induced
vortex lattice by expressing the BdG Hamiltonian in terms of superfluid
velocity and Berry's gauge fields. The two calculations are shown to agree with
each other. We then analyze quantitatively, the effects of anisotropic
dispersion to the scaling properties of vortex lattice and show that the vortex
lattice spacings will scale as $d'_y\sim s^{-\eta}d'_x $ where $1/2\leq
\eta\leq1$ and $s\sim H^2/3$ as compared to $\eta=1/2$ from dimensional scaling
analysis of non-vortex state. A very crucial prediction is also made on an
upper bound to the value of 'anomalous dimension' $\delta$ of density of states
scaling with magnetic field which we find to be $\delta\leq1/2$, a quantity
that could not be determined conclusively by previous purely analytical works
and a quantity that can be measured experimentally.
