Dynamical scaling properties of a one-dimensional Phi ⁴ lattice model-comparison with mode coupling theory

The dynamical scaling behaviour of the displacement-displacement correlation function of the one-dimensional Phi ⁴ lattice model is analysed by use of molecular dynamics simulations. The existence of a crossover temperature where relaxation times drastically increase suggests possible applicability of mode coupling theory (MCT) describing freezing processes in undercooled liquids. The authors find two independent dynamical scaling regions (two master functions describing the time evolution of the correlator) in accordance with MCT. A quantitative comparison of the MCT predicted scaling laws with the calculated ones for the Phi ⁴ model shows significant non-applicability of MCT especially for the beta relaxation process.