Only few available interatomic interaction potentials implement the α ↔ γ phase transformation in iron by featuring a stable low-temperature bcc and high-temperature fcc lattice structure. Among these are the potentials by Meyer and Entel (1998 Phys. Rev. B 57 5140), by Müller et al (2007 J. Phys.: Condens. Matter 19 326220) and by Lee et al (2012 J. Phys.: Condens. Matter 24 225404). We study how these potentials model the phase transformation during heating and cooling; in order to help initiating the transformation, the simulation volume contains a grain boundary. For the martensitic transformation occurring on cooling an fcc structure, we additionally study two potentials that only implement a stable bcc structure of iron, by Zhou et al (2004 Phys. Rev. B 69 144113) and by Mendelev et al (2003 Philos. Mag. 83 3977). We find that not only the transition temperature depends on the potential, but that also the height of the energy barrier between fcc and bcc phase governs whether the transformation takes place at all. In addition, details of the emerging microstructure depend on the potential, such as the fcc/hcp fraction formed in the α → γ transformation, or the twinning induced in and the lattice orientation of the bcc phase in the γ → α transformation.