Percolation Theory

This lecture covers the concept of percolation theory, focusing on the behavior of absorbed polymers on a boundary, the formation of giant molecules in polymer melts, and the phase transition in percolation models. It also discusses bond percolation, the probability of occupied bonds, and the existence of spanning clusters. The lecture delves into the scaling theory near critical points, the scaling assumptions, and the universal scaling behavior in percolation. Furthermore, it explores the characteristic scales for clusters, the dominant terms in percolation, and the expression of exponents in terms of critical points. The presentation concludes with the illustration of scaling assumptions, the scaling theory near critical points, and the expression of exponents in percolation.