Simulation methods in statistical physics

The Monte Carlo Method

• random number generators
• sampling stochastic variables

• Markov chains
• Ergodicity and (super) detailed balance
• Generative models
• Data analysis 

Critical phenomena 

• Finite-size scaling
• Self-avoiding walks

Ensembles

• simulations in the microcanonical ensemble
• simulations in the canonical ensemble
• simulations in the isobaric-isothermal ensemble
• simulations in the grand-canonical ensemble
• the Gibbs ensemble
• biased sampling
• free energy and density of states calculations

Molecular Dynamics

• symplectic integrators
• Nosé–Hoover thermostat

Understanding of the principal simulation techniques (Monte Carlo and Molecular Dynamics) used in Statistichal Mechanics.

Ability to design and implement algorithms to sample probability distributions.

classroom teaching

theoretical and exercice (including programming) classes

Contribution to the teaching profile

1.4 1.3 and 1.2

References, bibliography, and recommended reading

D. E. Knuth, The art of computer programming (chapter 3), Addison Wesley
A. Sokal, Monte Carlo Methods in Statistical Mechanics: Foundations and New Algorithms. In: DeWitt-Morette C., Cartier P., Folacci A. (eds) Functional Integration. 
D. Frenkel and B. Smit Understanding Molecular Simulation: From Algorithms to Applications, Elsevier
D. P. Landau and K. Binder A guide to Monte Carlo simulations in statistical physics, Cambridge university press 

Contacts

Bortolo.Matteo.Mognetti@ulb.be

Campus

Plaine

Method(s) of evaluation

• Other

Other

A Oral examination

B Study and presentation of a scientific article relevant for the course

Mark calculation method (including weighting of intermediary marks)

A 70%

B 30%

Language(s) of evaluation

• french
• english