Date of Completion
The Monte Carlo method is a broad class of random sampling techniques. One facet of its power arises in its ability to compute complex multidimensional integrals simply through large sample sizes. In this paper, we explore the use of Monte Carlo techniques and their advantage in modeling physical statistical systems such as the Ising model, Feynman path integrals and lattice QCD. The Metropolis algorithm, one type of Monte Carlo method, is applied to evolve these systems while other methods are used to compute and measure different observables. What we will see is that these measurements are an accurate representation of the real-world counterpart whose error arises from simplifying assumptions made on the models, approximations of the measurements and the finite simple sizes. These above sources of error can be rectified by more accurate models and larger sample size, the former of which we will see in modeling of lattice QCD.
Scott, Jacob L., "Monte Carlo Applications and Lattice QCD" (2016). Honors Scholar Theses. 469.