APPENDIX A
COMPUTER SIMULATION: DESIGN
In this chapter we discuss the software and code used in the Monte Carlo simulation.
Well known deterministic numerical methods are not discussed in any detail as such
studies are systematically described in regular textbooks on the subject [23]. Similar
systematic treatment of the use of stochastic methods in physics can be found in
textbooks as well [19, 20] but since our implementation is novel we do discuss it in
quite some detail.
A.1 Object Oriented Approach, Software Design
A.1.1 Basic Ideas
Our computer representation of a Lightcone World Sheet model will involve the
lattice, labelled by i 1, 2,... M and j = 1, 2,... N and the fields living on it. One
field will be present in any Lightcone World Sheet model, namely the "spins" whose
state determines the topology of the underlying Feynman diagram. This is the basic
building block of the computer model. The simulation method used here, based on the
Metropolis algorithm as explained in section 4.1 is to traverse the lattice in some way
visiting sites sequentially. At each site one offers local flips of spins and changes in the
field configuration with a probability obtained from the physical action. The calculation of
this probability is rather computationally intensive as a function of the values of fields and
spins in the vicinity of the site in question. One full traverse of the lattice, when all sites
have been visited once, is called a sweep The state of the system between sweeps, that
Sometimes a sweep means that as many visits have been made as there are lattice
sites. If sites are visited in a random order this could mean that a sweep is done while
some lattice sites have never been visited and others have been visited more than once,