Abstract
The Renormalisation group is a key to understand various subjects in modern physics. Originally, it was developed by Feynman to calculate infinities in quantum field theory, for example, gyromagnetic ratio in quantum electrodynamics. It was considered just a useful tool for computing QFT. However, after Kadanoff first studied the block-spin method, renormalisation is understood as a coarse-graining of degrees of freedom. This idea was more developed by Wilson to renormalisation group. Wilson’s idea is regarded as a modern way to understand renormalisation. Now, physicists utilise the Wilson renormalisation group in high-energy physics, condensed matter, statistical physics, etc. For instance, it gives intuitions of effective field theory in high-energy physics, phase transition, and critical phenomena in statistical physics and condensed matter theory. In this lecture series, we will discuss basic thermodynamics and mean-field theory for the Ising model. We will develop our discussion by promoting order parameters into fields. This procedure naturally introduces the path integral formalism. In terms of the path integral formalism, we can interpret the phase transition of the system as a renormalisation group. From this lecture series, we will hopefully understand the renormalisation and critical phenomena in a modern way.