## Admission Requirements

Bachelor in Physics and knowledge of basic statistical mechanics.

## Description

The course provides an introduction to phase transitions and critical phenomena in equilibrium systems and represents the first part of a two-part introductory courses on emergent phenomena in equilibrium and non-equilibrium statistical physics. The second (elective) part of this course is given in Statistical Physics b and is focused on emergent phenomena in non-equilibrium systems (i.e. collective motion in animals and other biological systems etc.)

Topics

• Introduction to phase transitions and critical phenomena in statistical mechanics.

• The one-dimensional Ising model: exact solution via transfer matrix method.

• The two-dimensional Ising model: domain walls and Peierls’ argument.

• Mean field theory.

• Fluctuations theory and field-theoretical approach to critical phenomena.

• Universality, scaling and critical dimensions.

• Real-space renormalization group.

• Momentum-shell renormalization group and ε-expansion.

## Course Objectives

The aim of the course is develop a strong foundation in advanced statistical mechanics with an emphasis on emergent phenomena. Furthermore, the course aims to provide the students with a toolbox of mathematical techniques that can be readily used in theoretical and experimental research projects.

## Timetable

## Mode of instruction

Lectures and tutorials.

## Assessment method

Final exam with open questions and homework assignments for bonus points.

## Blackboard

To have access to Blackboard you need a ULCN-account.Blackboard UL

## Reading list

Nigel Goldenfeld, Lectures of phase transitions and the renormalization group (Perseus Books, 1992).

## Contact

Lecturer: Dr. Luca Giomi