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/${\mathit{t}}^{\mathrm{\delta }}$ (A,P,δ>0) in the self part of the intermediate scattering function ${\mathit{F}}_{\mathit{s}1}$(k,t). In agreement with MCT we find that the diffusion constant for one of the two types of particles, the relaxation times of ${\mathit{F}}_{\mathit{s}1}$(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-${\mathit{T}}_{\mathit{c}}$ ${)}^{\gamma }$, for T>${\mathit{T}}_{\mathit{c}}$ at constant density. As predicted by the theory the critical temperatures ${\mathit{T}}_{\mathit{c}}$ 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.