Discrete quantum field theory = problem in equilibrium
statistical mechanics. Example: 2D scalar field theory on the lattice
Partition function as a probability distribution
Markov processes, master equations as a way of realizing such
distributions. Stochastic estimation of observables -- the Monte Carlo
method
Simple metropolis algorithm -- the all purpose workhorse
Introduction to phase transitions and critical phenomena. Finite size scaling.
Heatbath and overrelaxation -- more efficient (local) algorithms
Cluster techniques to tackle critical slowing down
Classical dynamics and Langevin methods for continuous systems.
Hybrid method -- application to non-local systems such as relativistic
fermions. Fourier acceleration.
Simple error analysis and fitting techniques
Techniques for solving large sparse linear problems
Elementary ideas about the RG. Introduction to MCRG.
Other physics topics: lattice gauge theories, spin systems,
random systems
In each case I shall try to include a self-contained introduction to
the physics problem/system,
an explanation of the algorithm used and a code (C++) that can be used
to implement
that algorithm. Small scale working demonstrations of such codes
will be used throughout to illustrate computational issues. Some
familiarity with
C/C++ will be assumed although a student with minimal programming
skills should
be able to learn more advanced programming concepts as the course
progresses.
I may set (small) homework exercises during the semester but will
additionally
require students to undertake a substantial computational project in
the last 1/3 of
the semester.