Complex Physics

Course content

The topics that will be covered are: Phase transitions, Ising model, critical phenomena, Monte Carlo simulations, Percolation, Self organization, Networks, Epidemic models, scale free phenomena, and econophysics.


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

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.

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



The student is expected to gain basic knowledge on contemporary research in complex systems.

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.



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 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 theoryand 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.

lectures and exercises

lecture notes

Students would gain by having taken a course on Dynamical Systems and Chaos, as well as by having some knowledge of statistical mechanics.
These requirements are non-mandatory, and with additional effort the course can
also be followed by students with background in mathematics, bio-informatics,
economics or computer sciences.
As a minimum the students are expected to have Python or Matlab on their laptop
and be able to write a program that simulates a first order differential equation.

The course 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 and computer 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.

Continuous feedback during the course of the semester
Feedback by final exam (In addition to the grade)
7,5 ECTS
Type of assessment
Continuous assessment
Oral examination, 30 minutes
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)
Without aids
Marking scale
7-point grading scale
Censorship form
No external censorship
Several internal examiners
Criteria for exam assessment

see learning outcome

Single subject courses (day)

  • Category
  • Hours
  • Lectures
  • 24
  • Preparation
  • 131
  • Theory exercises
  • 28
  • E-Learning
  • 2,5
  • Exam
  • 20,5
  • English
  • 206,0


Course number
7,5 ECTS
Programme level
Full Degree Master

1 block

Block 1
Study Board of Physics, Chemistry and Nanoscience
Contracting department
  • The Niels Bohr Institute
Contracting faculty
  • Faculty of Science
Course Coordinator
  • Kim Sneppen   (7-78736a75756a734573676e33707a336970)

Jan Haerter
Mogens Høgh Jensen

Saved on the 29-04-2021

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