Lecture: Introduction to Monte Carlo simulation methods

Dates

WS 23/24: 11.-18.03.2024

Abstract

Programming course and exercises. Introduction to Monte-Carlo methods up to simulations of Yang-Mills-Theories.

Preliminary outline

First part

• Ising model simulations.
• Ising model and related theories, low and high temperature expansions, simulation algorithms

Second part

• Gauge principle and gauge theories in the continuum, formulation of pure gauge theory on the lattice.
• Simulation algorithm for SU(2) pure gauge theory, implementation of SU(2) metropolis algorithm

Material

Lecture 1

Exercises 1

Lecture 4

Exercises 2

This exercise is to write a simple metropolis update code for SU(2) pure gauge theory. In order to simplify the task, several routines for handling configurations, links, matrices, and random numbers are already provided.
C++ and Fortran code as a staring point for the exercise of SU(2) pure gauge lattice simulations.
For the C++ program you have to call "make Eigen" first. Additional dependence: Boost library (please install on your system).

Literature / References

• Many different examples for Ising model simulations in various programming languages are avaiable online.
• Wipf, "Statistical Approach to Quantum Field Theory", Springer (2013)
• The following books contain further information on simulations of pure gauge theory on the lattice:
• Gattringer, Lang, "Quantum Chromodynamics on the Lattice", Springer (2010)
  
• Montvay, Münster, "Quantum Fields on a Lattice", Cambridge University Press (1994)
• Smit, "Introduction to Quantum Field on a Lattice", Cambridge Lecture Notes in Physics (2002)
• Rothe, "Lattice Gauge Theories An Introduction" World Scientific (2005)