Abstract

What goes on at the liquid-solid phase transition in glass is one of the big open questions in physics. It is neither a continuous nor a discontinuous transition, but rather is a combination of both: a mixed phase transition. In order to better understand it, the universality class of this transition needs to be explored (assuming there is one). Percolation is one of the simplest models to exhibit a phase transition, so it makes for a good starting point. I will discuss models related to percolation that indeed exhibit a mixed transition, with a jump in the order parameter but with a diverging correlation length. Furthermore, I will explain how this transition comes about.

In the second half I will present some results concerning random walk on percolation clusters at the phase transition. Random walk is a process that can be used to describe the random movement of particles. The average speed of random walks on critical clusters is very low, because of their fractal-like structure. I will explain how the structure causes the slowness of random walk.