  Considerations of the bad-metal behavior led to an early proposal for a
quantum critical point under a P for As doping in the iron pnictides, which has
since been experimentally observed. We study here an effective model for the
isoelectronically tuned pnictides using a large-$N$ approach. The model
contains antiferromagnetic and Ising-nematic order parameters appropriate for
$J_1$-$J_2$ exchange-coupled local moments on an Fe square lattice, and a
damping caused by coherent itinerant electrons. The zero-temperature magnetic
and Ising transitions are concurrent and essentially continuous. The
order-parameter jumps are very small, and are further reduced by the
inter-plane coupling; quantum criticality hence occurs over a wide dynamical
range. Our results provide the basis for further studies on the quantum
critical properties in the P-doped iron arsenides.
