On the applicability of mode coupling theory to a phi(4)-model with first order phase transition

A phi(4)-model with symmetric double-well-like on-site potential and anharmonic, infinite range interactions is investigated. This model exhibits a first order phase transition at a temperature T-c. The time-dependent displacement correlation function is studied in the framework of the mode coupling theory (MCT). Depending on the choice of slow modes, MCT makes qualitatively different predictions which are compared with MD-results. These numerical results suggest that only the order parameter mode (x) over tilde(q = 0), should be considered as slow. In that case it is shown that MCT yields a dynamical transition in the supercooled high-temperature phase ([<(x)over tilde (q = 0)>] = 0) at a temperature T* which coincides with the spinodal temperature T-s (T-s = 0 for our model) where the metastable supercooled phase becomes instable.