NFYK18005U Complex Physics

Volume 2022/2023

MSc Programme in Nanoscience
MSc Programme in Physics
MSc Programme in Physics with a minor subject


The topics that will be covered are: Equilibrium physics with Phase transitions and Ising model,  Monte Carlo simulations, critical phenomena, Scale free systems, Percolation, Self organization, Networks, Stochastic simulations, Agent based models, Econophysics.

Learning Outcome


The aim is to learn how to rephrase a complex phenomenon into a mathematical equation or computer algorithm.

At the conclusion of the course students should be able to develop computer programs that implement and analyse simple quantitative models of stochastic systems with many parts.

The student will learn to implement agent based models, and learn about the advantages of this type of approach to a range of phenomena.

Students will learn to appreciate that the joint dynamics of a many body system often is both quantitatively and qualitatively different from the simple sum of its parts.


The student is expected to gain basic knowledge on contemporary research in complex systems.
In particular the course emphasize the concept of universality and that the behaviour in many large dynamical systems share common features.

This includes the ability to use fundamental concepts from statistical mechanics, non-linear dynamics, time series analysis, stochastic dynamics and self-organizing systems. These topics give understanding of scaling and scale-invariant phenomena, including fractals and scale-free networks.

The course show many examples on non-equilibrium systems that self-organize to a steady state dynamics that is characterized by fractals and power laws.


How to model and analyse systems with many components in terms of equations and computer programs.

Write computer models of systems with many interacting parts, including the Ising model, Monte-Carlo simulations, percolation, networks, stochastic dynamical systems, and models of disease spreading.

Implement models to describe self-organized dynamics of structures, for example within network theory and for systems that behave similar across a wide range of scales.

The course will provide the students with tools from physics that have application in a range of fields within and beyond physics.

lecture notes

As a minimum the students are expected to have Python on their laptop and furthermore to be able to write a program that perform simple matrix manipulations (multiplications or addition).
They should also to be able to program the dynamics of a first order differential equation. The students should know how to represent simulation results visually. Students should also
know Taylor expansions and know the concept of eigenvalues of a matrix.

Students would gain by having taken a course on Dynamical Systems and Chaos,
and having basic knowledge of statistical mechanics.
These course requirements are non-mandatory, and with additional effort the course can
also be followed by students with background in mathematics, bio-informatics,
nano-science, computational chemistry, economics or computer sciences.
lectures and exercises
The course is also suited for physics students who plan to write their thesis within complex systems, biological physics or quantitative models of biological systems.
Students from mathematics, bio-informatics, economics, computer science, chemistry and nano-science are welcome.

The course is identical to the discontinued course NFYK15018U Topics in Complex Systems. Therefore you cannot register for NFYK18005U Complex Physics, if you have already passed NFYK15018U Topics in Complex Systems.
If you are registered with examination attempts in NFYK15018U Topics in Complex Systems without having passed the course, you have to use your last examination attempts to pass the exam in NFYK18005U Complex Physics. You have a total of three examination attempts.
  • Category
  • Hours
  • Lectures
  • 24
  • Preparation
  • 131
  • Theory exercises
  • 28
  • E-Learning
  • 2,5
  • Exam
  • 20,5
  • Total
  • 206,0
Continuous feedback during the course
Feedback by final exam (In addition to the grade)
7,5 ECTS
Type of assessment
Continuous assessment
Oral examination, 20 minutes
Type of assessment details
The exam evaluation consists of two parts;
Two mandatory assignments during the course (each counting 10% of the final grade)
Oral exam without preparation time (counting 80% of the final grade)
The parts of the exam do not need to be passed separately.
Without aids
Marking scale
7-point grading scale
Censorship form
No external censorship
Several internal examiners

Oral exam 30 minutes (covering also the topics of the home assignments)

Criteria for exam assesment

see learning outcome