## 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

You will find the timetables for all courses and degree programmes of Leiden University in the tool MyTimetable (login). Any teaching activities that you have sucessfully registered for in MyStudyMap will automatically be displayed in MyTimeTable. Any timetables that you add manually, will be saved and automatically displayed the next time you sign in.

MyTimetable allows you to integrate your timetable with your calendar apps such as Outlook, Google Calendar, Apple Calendar and other calendar apps on your smartphone. Any timetable changes will be automatically synced with your calendar. If you wish, you can also receive an email notification of the change. You can turn notifications on in ‘Settings’ (after login).

For more information, watch the video or go the the 'help-page' in MyTimetable. Please note: Joint Degree students Leiden/Delft have to merge their two different timetables into one. This video explains how to do this.

## 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 registering for each course component. This can be done via Mystudymap. You do this twice a year: once for the courses you want to take in semester 1 and once for the courses you want to take in semester 2.

Registration for courses in the first semester is possible from July onwards; registration for courses in the second semester is possible from December onwards. For more information, see this page

Please note that it is mandatory for all students to register for their exams. This can be done up to and including 10 calendar days prior to the exam or up to five calendar days in case of a retake exam (retake registration opens 30 days before the retake takes place). You cannot participate in the exam or retake without a valid registration in My Studymap

## 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.