Phonon soft modes and para- to ferro-electric phase transitions

Abstract In this special issue of Physica A in memory of Professor Dietrich Stauffer, I first recall my impression on him while being his postdoc for a year at HLRZ. In the following scientific part, I discuss the theory of soft phonons with quartic nonlinear interactions. This is applied to the cubic crystal BaTiO 3 for phase transition from para- to ferro-electric phase.