## Admission Requirements

Bachelor in Physics and knowledge of basic statistical mechanics.

## Description

What do a magnet, a Bose-Einstein condensate and a flock of birds have in common? All these systems exhibit a collective behavior and have large-scale physical properties that cannot be understood in terms of a simple extrapolation of the properties of a few particles. Conversely, systems comprising many interacting subunits often present entirely new properties, that scientists refer to as emergent.

Statistical Physics A, is the first part of a two-part introductory course on emergent phenomena in equilibrium and non-equilibrium systems. The course provides an introduction to phase transitions and critical phenomena at equilibrium. 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.)

The course consists of 10 lectures and 5 tutorials (exercise classes), during which the students will practice the concepts and the techniques learned during the lectures by solving problems.

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 to 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.

Specifically, at the end of the course, successful students will have learned how to:

Solve 1-dimensional spin models and calculate quantities of physical interests such as the average magnetization, magnetic susceptibility, energy, entropy etc.

Set up a mean-field theory for the Ising model and analogous models and use it to calculate the critical exponents.

Recognize the scale-invariance and how it connects with second order phase transitions.

Construct a field theory for magnetism by perfuming the continuum limit of the mean-field Ising model and use it to calculate the spin-spin correlation function and other relevant quantities.

Apply Wilson’s renormalization group, in real and Fourier space, to go beyond mean-field and accurately describe the critical behavior of ferromagnets.

## Timetable

Physics Schedule

For detailed information go to Timetable in Brightspace

In MyTimetable, you can find all course and programme schedules, allowing you to create your personal timetable. Activities for which you have enrolled via MyStudyMap will automatically appear in your timetable.

Additionally, you can easily link MyTimetable to a calendar app on your phone, and schedule changes will be automatically updated in your calendar. You can also choose to receive email notifications about schedule changes. You can enable notifications in Settings after logging in.

Questions? Watch the video, read the instructions, or contact the ISSC helpdesk.

**Note:** Joint Degree students from Leiden/Delft need to combine information from both the Leiden and Delft MyTimetables to see a complete schedule. This video explains how to do it.

## Mode of instruction

See Brightspace

## Assessment method

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

## Reading list

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

## Registration

As a student, you are responsible for enrolling on time through MyStudyMap.

In this short video, you can see step-by-step how to enrol for courses in MyStudyMap.

Extensive information about the operation of MyStudyMap can be found here.

There are two enrolment periods per year:

Enrolment for the fall opens in July

Enrolment for the spring opens in December

See this page for more information about deadlines and enrolling for courses and exams.

**Note:**

It is mandatory to enrol for all activities of a course that you are going to follow.

Your enrolment is only complete when you submit your course planning in the ‘Ready for enrolment’ tab by clicking ‘Send’.

Not being enrolled for an exam/resit means that you are not allowed to participate in the exam/resit.

## Contact

Lecturer: Dr. Luca Giomi

## Remarks

**Transferable skills**

At the end of the course, students will have been trained how to:

Decompose a complex concept into simpler steps, each of which can be rationalized at an intuitive level.

Think across individual academic disciplines and use analogies with other fields (e.g. computer graphics) to build up physical intuition.

Not to stop after the first hints of success, but aim at greater goals.

**Software**

Starting from the 2024/2025 academic year, the Faculty of Science will use the software distribution platform Academic Software. Through this platform, you can access the software needed for specific courses in your studies. For some software, your laptop must meet certain system requirements, which will be specified with the software. It is important to install the software before the start of the course. More information about the laptop requirements can be found on the student website.