Examples of renormalization

For more than half a century, the renormalization group has been one of the most widely used approaches in statistical physics for trying to link the microscopic world to the macroscopic world. It provides a means of explaining the universality of critical behaviors observed during phase transitions, and of systematically calculating the exponents and functions that characterize these critical behaviors. It also enables us to tackle many other issues, such as the transition to chaos, growth problems and disorder. The aim of this lecture is to illustrate the main ideas behind this approach with the simplest possible examples.