CENTRAL PEAK FOR A SCALAR PHI(4)-MODEL - MODE-COUPLING APPROACH REVISITED

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 phi(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 f rom a perturbational treatment of the renormalized vertices. Again, th is mode coupling approach may yield a dynamical transition at a temper ature T-c(')(greater than or equal to T-c) at which the dynamics becom es nonergodic, i.e. a central peak occurs. For a phi(4)-model with inf inite range interactions our theoretical predictions are consistent wi th numerical results. Furthermore, if the fluctuations in the vicinity of T-c are Gaussian, no dynamical transition occurs above T-c. Theref ore the temperature T-O'obtained from the Ginzburg criterion sets an u pper bound for T-c'. If a dynamical transition occurs, it is shown tha t the nonergodicity parameter as function of wave vector q and tempera ture T follows from an universal master function.