Global phase diagram for magnetism and lattice distortion of iron-pnictide materials

We study the global phase diagram of magnetic orders and lattice structure in the Fe-pnictide materials at zero temperature within one unified theory tuned by both electron doping and pressure. On the low doping and high-pressure side of the phase diagram, there is one single transition, which is described by a z=2 mean-field theory with very weak run-away flows; on the high doping and low-pressure side, the transition is expected to split to two transitions, with one O(3) spin-density wave transition followed by a z=3 quantum Ising transition at larger doping. The fluctuation of the strain field of the lattice will not affect the spin-density wave transition but will likely drive the Ising nematic order transition a mean-field transition through a linear coupling, as observed experimentally in BaFe2-xCoxAs2.