Glassy behaviour in a two-dimensional lattice gas model with asymmetric particles

We study the relaxation process in a two-dimensional lattice gas model, where the interactions arise from the excluded volume. In this model particles have three arms with an asymmetric shape, which results in geometric frustration that inhibits full packing. A dynamical crossover is found at the arm percolation of the particles, from a dynamical behaviour characterized by a single step relaxation above the transition, to a two-step decay below it. Relaxation functions of the self-part of density fluctuations are well fitted by a stretched exponential form, with a beta exponent decreasing when the temperature is lowered until the percolation transition is reached, and constant below it. The dynamical nonlinear susceptibility, defined as the fluctuation of the self-overlap autocorrelation, exhibits a peak at some characteristic time, which seems to diverge at the maximum density as well.