  Free nodal fermionic excitations are simple but interesting examples of
fermionic quantum criticality in which the dynamic critical exponent $z=1$, and
the quasiparticles are well defined. They arise in a number of physical
contexts. We derive the scaling form of the diamagnetic susceptibility, $\chi$,
at finite temperatures and for finite chemical potential. From measurements in
graphene, or in $\mathrm{Bi_{1-x}Sb_{x}}$ ($x=0.04$), one may be able to infer
the striking Landau diamagnetic susceptibility of the system at the quantum
critical point. Although the quasiparticles in the mean field description of
the proposed $d$-density wave (DDW) condensate in high temperature
superconductors is another example of nodal quasiparticles, the crossover from
the high temperature behavior to the quantum critical behavior takes place at a
far lower temperature due to the reduction of the velocity scale from the fermi
velocity $v_{F}$ in graphene to $\sqrt{v_{F}v_{\mathrm{DDW}}}$, where
$v_{\mathrm{DDW}}$ is the velocity in the direction orthogonal to the nodal
direction at the Fermi point of the spectra of the DDW condensate.
