How many quantum phase transitions exist inside the superconducting dome of the iron pnictides?

Recent experiments on two iron-pnictide families suggest the existence of a single quantum phase transition (QPT) inside the superconducting dome despite the fact that two separate transition lines - magnetic and nematic - cross the superconducting dome at $T_{c}$. Here we argue that these two observations are actually consistent. We show, using a microscopic model, that each order coexists with superconductivity for a wide range of parameters, and both transition lines continue into the superconducting dome below $T_{c}$. However, at some $T_{\mathrm{merge}}<T_{c}$, the two transitions merge and continue down to T=0 as a single simultaneous first-order nematic/magnetic transition. We show that superconductivity has a profound effect on the character of this first-order transition, rendering it weakly first-order and allowing strong fluctuations to exist near the QPT.