Central peak for a scalar ϕ 4-model: mode coupling approach revisited

Abstract

We reinvestigate the mode coupling approach to the central peak which occurs in the vicinity of a structural phase transition at T c. For a scalar ϕ 4-model it is shown that the use of renormalized vertices leads to quite different results compared to recent calculations with bare vertices. Particularly, we prove that the latter are obtained in leading order of the anharmonicity constant of the on-site potential from a perturbational treatment of the renormalized vertices. Again, this mode coupling approach may yield a dynamical transition at a temperature T c'(≥ T c) at which the dynamics becomes nonergodic, i.e. a central peak occurs. For a ϕ 4- model with infinite range interactions our theoretical predictions are consistent with numerical results. Furthermore, if the fluctuations in the vicinity of Tc are Gaussian, no dynamical transition occurs above Tc. Therefore the temperature T 0'obtained from the Ginzburg criterion sets an upper bound for T c'. If a dynamical transition occurs, it is shown that the nonergodicity parameter as function of wave vector q and temperature T follows from an universal master function.