In this paper we study phase transition phenomena in an independent edge percolation model on a d-dimensional hyper-cubic lattice. The subject is treated in a rigorous, self-contained and accessible way for undergraduate students in physics and related areas. These models are often used to describe situations of physical interest. The "percolation phenomena" occur when we find an infinite cluster in the lattice. The change from a state where there are only finite clusters to a state with at least one infinity cluster is the geometric analogous of a phase transition as known in statistical mechanics. We show that the phase transition occurs, for hyper-cubic lattices in dimension d > or = 2, in a well-defined point, known as the critical point. We can associate an order parameter to this phase transition. Among all the physical models that present a phase transition, the percolation model is probably one of the simplest. At the same time, it is a good example of the connection that sometimes we find relating physics, mathematics and probability.
