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Academic year
Didactic period
Secondo Semestre

Training objectives

This course provide basic knowledge and helps acquire the computational skills relevant for Monte Carlo simulations of complex systems; the course will cover in depth the statistical and critical properties of spin systems.


- Basic concepts on quantum mechanics as obtained in the undergraduate course on Quantum mechanics
- Basic concepts of thermodynamics and statistical physics, as obtained in undergraduate courses in Condensed Matter
- Basic skills in programming (C-language or Mathematica or similar pachages)

Course programme

The main topics covered in this course are as follows:
- Preliminary examples: random motion, its correlation functions and generating functions
- Pseudo-random numbers and algorithms to generate pseudo-random numbers
- Markov chains and their applications to Real Space Monte Carlo methods
- A survey of the main Monte Carlo methods: Metropolis, Heat-Bath, Overrelaxed
- Re-weighting techniques
- Survey of the main techniques for error analysis of Monte Carlo data
- Overview of the main spin models: Ising, Potts, Heisenberg
- Analytical approximations to solve spin systems: high-temperature and low-temperature expansions, mean field theories
- An overview of the real-space renormalization group
- An overview of finite size scaling
- Simulation and analysis of the critical properties of spin models.

Didactic methods

The course is based on lectures, covering the various topics of the course syllabus. Approximately 50% of all lectures will focus on actual work carried out by the students, under the guidance of the instructor. Students will develop the details of the simulation algorithms, write the corresponding program codes and analyze simulation results.

Learning assessment procedures

The oral exam will be based on the discussion of a report and a presentation by the student; in this presentation the student will report his results on a subject agreed with the instructor in the final stages of the course. This discussion will be used to assess the knowledge and the skills developed by the student.

Reference texts

- K. Binder, D.W. Heermann, Monte Carlo Simulation in Statistical Physics
- Barone, Marinari, Organtini, Ricci Tersenghi, Scientific Programming: C-Language, Algorithms and Models in Science