OVERVIEW

The most important computer simulation methods in condensed matter physics are presented and applied to specific exercises. Each student is asked to write down the simulation codes for these exercises and to analyze the outcome of the simulations.

AIMS AND CONTENT

LEARNING OUTCOMES

Learning the basic theory of the most important computer simulation methods in statistical physics.  Acquiring the skills needed to independently develop simulation programs applied to complex physical problems in statistical physics and condensed matter physics.

TEACHING METHODS

Lectures and programming sessions.

SYLLABUS/CONTENT

Generalities on computer simulations.

Monte Carlo Method - Simple sampling and importance sampling. Markov chains. Conditions for convergence at equilibrium. Detailed balance. Metropolis algorithm. Monte Carlo step. Application to the two-dimensional lattice gas on a square lattice. Order Parameter. Order-disorder phase transitions. Continuous time Monte Carlo. Application to the growth of islands in two dimensions. Mean field theory for island counting. Fractal dimension.

Molecular Dynamics - Structure of a classical Molecular Dynamics program. Microcanonical simulations. Preparing the initial configuration. Algorithms for propagating the trajectories. Euler algorithm. Verlet algorithm. Leapfrog and velocity verlet algorithms. Canonical simulations. Andersen Thermostat. Simulation of a cluster of argon atoms.

RECOMMENDED READING/BIBLIOGRAPHY

Lecture notes

TEACHERS AND EXAM BOARD

LESSONS

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

ASSESSMENT METHODS

The oral exam is always conducted by the responsible professor and by an expert in the subject (usually a tenured professor) and has a duration between 25 and 40 minutes.

In the first part of the exam, the student shows, with the help of slides, the results obtained by a specific simulation program that she/he has personally developed after agreement with the teacher. In the second part of the exam, the student is asked a question about the contents of the part of the course not directly related to the simulation presented before (for example, if a Monte Carlo simulation is presented in the first part, the question will focus on molecular dynamics).