Relaxation dynamics in a lattice gas: A test of the mode-coupling theory of the ideal glass transition

By means of computer simulations we investigate the dynamical behavior of a binary lattice-gas mixture with short-range interactions in order to provide a stringent test of mode-coupling theory (MCT). The dynamics of the particles is given by Monte Carlo--like moves that change the positions of the particles and binary collisions that change the velocities. By monitoring the self part of the van Hove correlation function we find the low-temperature dynamics to be glasslike. In accordance with MCT the imaginary part of the dynamic susceptibility {χ}'' shows a well-defined {α} peak whose high-frequency wing follows a von Schweidler law with an exponent that is independent of temperature. The low-frequency wing of the peak follows a different power-law dependence that corresponds to a power law of the form -P+A/t^δ (A,P,{δ}>0) in the self part of the intermediate scattering function Fₛ₁(k,t). In agreement with MCT we find that the diffusion constant for one of the two types of particles, the relaxation times of Fₛ₁(k,t), the location of the {α} peak in the susceptibility, and the prefactor of the von Schweidler law all have a power-law dependence on temperature, (T-Tc{)}^{{γ}}$, for T>${T}c$ at constant density. As predicted by the theory the critical temperatures ${T}c$ for the different quantities are the same within the statistical error. However, in contradiction to MCT, the critical exponents {γ} vary from one quantity to another.The value of the Lamb-M\"ossbauer factor shows qualitatively the wave-vector dependence predicted by MCT. The self part of a second kind of correlation function exhibits the two power laws predicted by MCT for the high- and low-frequency wings of the {β} relaxation. We show that in the vicinity of the minimum of the susceptibility the scaling behavior predicted by MCT holds. However, the location of this minimum at a given temperature depends on the quantity investigated, contrary to the predictions of MCT. Moreover, the value of {χ}'' at this minimum exhibits a power-law dependence on temperature with an exponent that is significantly larger than the one predicted by MCT. We also find that the height of the {α} peak as well as the total energy per particle have a power-law dependence on temperature and that the corresponding critical temperatures are close to those obtained for the other quantities.