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Project 2 - Monte Carlo simulations

Introduction

For the second project, you will choose one out of three different projects that describe very different physics, but that are all tackled with one type of technique: the Monte Carlo method. Your possible choices are:

  1. Monte-Carlo simulation of the Ising-model
    The Ising model is a simple model for (anti-)ferromagnetism. In this project you can study the physics of phase transitions, explore topics you learn in Advanced Statistical Mechanics (such as critical exponents), or implement advanced algorithms.

  2. Variational Quantum Monte Carlo
    In this project you will calculate the ground state energy of a Helium atom. This is the simplest interacting quantum system (two electrons that not only feel the Coulomb interaction with the nucleus, but also amongst themselves), but cannot be solved analytically any more. You solve the problem on the computer approximately with a combination of Monte Carlo integration and the variational method.

  3. Monte Carlo simulation of polymers
    Polymers are long chains of atomic constituents. Like a thread of wool, they usually don't stay straight, but they curl up. This curling-up is influenced on how the consitutents of the polymer interact. In this project you will investigate these properties quantitatively.

Instructions

What we expect you to do

Again, work in groups of two or three students. You may work with the same group as in project 1 or choose new partners.

Choose one of the three possible projects. As for the first project, we expect you to write a well-structured simulation code, validate it, generate simulation results in an organized fashion and summarize them in a proper scientific report.

Unlike the first project, we however give you more freedom and responsibility. The lecture notes only give an introduction, and we expect you to study the details on your own using the provided literature.

The second project is shorter in duration than the first project (4 weeks instead of 6)! This is because (i) you are now more experienced but also (ii) because the second project is actually less extensive than the first one.

Milestones along the path

Like in the first project, we expect you to document your progress with respect to weekly milestones. Unlike the first project however, we will only provide you broad weekly goals. You will then first work out detailed milestones for yourself, and then report your progress with respect to those.

Resources

  • Materials covered in the lectures. These are also summarized in the lecture notes.
  • Literature for the Monte Carlo simulation of the Ising model:
    • The basics of the Ising model are explained in Chapter 7 from the book "Computational Physics" by Jos Thijssen,
    • basics of the Monte Carlo simulation of the Ising model in Chapter 10
    • details about advanced algorithms in Chapter 15.5.
  • Literature for the Variational Monte Carlo method:
  • Literature for the Monte Carlo simulation of polymers:
  • Feel free to search for any help/code snippets/ideas you can find on the internet (but be sure to reference them properly!). We definitely encourage you to use Numpy/Scipy/...!

Products

  • Simulation code in a gitlab repository
  • Report
  • Filled out weekly progress issues. These will be opened automatically in your gitlab repository, and need to be filled in before the next class.

Assessment criteria

See the details of the grading scheme here

Supervision and help

  • The lecturers and the TAs are present during the lectures and are willing to help with all your problems
  • Out of class you are encouraged to ask any question on the course chat (preferred) or write an email to the lecturers.