The separation of dyanamics into slow and fast components for the one-dimensional ${\mathrm{\Phi }}^4$ lattice model with a nearest-neighbor interaction is studied. We find two dynamic scaling laws for the displacement-displacement correlator in the strong-interaction case. The temperature window where scaling appears has a nonzero lower bound. There exist no analogies between the found scaling properties and structural relaxation processes in undercooled liquids near the liquid-glass transition. This fact seems to be due to the presence of static on-site double-well potentials. In the case of weak interaction only one dynamic scaling law seems to appear.

• Received 29 September 1992

DOI:https://doi.org/10.1103/PhysRevB.47.14910