A performance study of a template C++ class for parallel Monte Carlo simulations of local statistical field theories on a three dimensional lattice

Abstract

In this thesis we investigate the performance properties of a template C++ class designed to run parallel Monte Carlo simulations of local statistical field theories on a three dimensional lattice. The generic nature of the class allows for data type flexi- bility when defining the mater fields at every site of the grid while incorporating this flexibility into a generic MPI exchange function to allow for correct data transfer in parallel simulations. This allows one to overcome the book-keeping issues associated with the parallel software development of code needed to run simulations of different field theories with different physical properties. We will investigate how the system performs in parallel by looking at its scaling behaviour for different matter fields and will examine the factors affecting its performance - particularly in relation to how the lattice is stored in memory and how this could influence an optimal choice of MPI decomposition. To test the performance of our class, we will run parallel sim- ulations of the 3D Ising model and investigate its critical behaviour by computing observables such as average magnetization per spin, magnetic susceptibility and its average energy. The case of a double precision data type on the lattice sites will then be tested by running simulations of φ4 quantum field theory in 2 + 1 dimensions using its discrete lattice action. We will run simulations in both the Ising limit and the limit of a free scalar field theory, and examine how the mass of a particle behaves as the action parameters are varied. We compare our results to that obtained in the literature and comment on the similarities to our Ising model results.