Directed Percolation

The term percolation (from the Latin percolare = to filter) means to make a liquid to pass through fine interstices and is often used in the context of filtering.¹ A filter is usually made of a porous substance such as cloth, paper, sand or charcoal, through which a liquid may be passed to cleanse it of the solid or impure matter held in suspension. The retained material accumulates, clogging the pores so that the filter becomes impermeable after some time and needs to be replaced. Therefore, it is important to understand how the transition from percolation to congestion takes place, and we shall use a particular formulation of this problem as a paradigm for absorbing phase transitions.