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We show theoretical results concerning solid-solid phase transitions in Fe induced by pressure at 0 K and by temperature at 0 GPa. One intermediate case for 300 K at 9.8 GPa is also considered. The interatomic potential employed has been shown to be capable of describing the martensite-austenite phase transition in iron. We study the phonon dispersion curves at 0 K, and their variation by pressure. After identifying a soft phonon mode, we determine the transition pressure using several techniques. From molecular-dynamics simulations we obtain the phonon dispersion curves for 0 and 9.8 GPa at 300 K. We also study the phonon softening by temperature. We find the vibrational Gibbs free energy and compare the transition temperature with the value found by using thermodynamic integration. A calculation of the vibrational entropy demonstrates that the inclusion of anharmonicities beyond the quasiharmonic …