Introduction to renormalization

TL;DR

This paper introduces the renormalization group approach to understanding critical phenomena in non-ideal systems, highlighting how it explains features like altered phase transitions and universality classes.

Contribution

It presents an accessible overview of renormalization concepts applied to complex systems with disorder, anisotropy, and frustration, illustrating their impact on critical behavior.

Findings

Renormalization explains softening of phase transitions.

Universality classes can change due to system peculiarities.

Effective critical behavior becomes more complex in non-ideal systems.

Abstract

In these lectures I discuss peculiarities of the critical behaviour of ``non-ideal'' systems as it is explained by the renormalization group approach. Examples considered here include account of the single-ion anisotropy, structural disorder, frustrations. I introduce main ideas of renormalization and show how it serves the explanation of typical features of criticality in the above systems: softening of the phase transition, changes in the universality class, complicated effective critical behaviour.