Particle Physics Seminar

Motivated by recent results demonstrating the applicability of machine learning techniques to quantum spin systems, we explore an application of the worm algorithm to the two dimensional Ising model. We begin by presenting the high temperature expansion of the Ising model, which is used to generate equilibrium configurations of "worms" represented as two¬dimensional greyscale images. From these configurations, we are then able to calculate physical quantities of interest. In particular, we are able to identify the logarithmic divergence of the specific heat at the critical temperature. We then propose a complementary approach using machine learning techniques (in particular, principal component analysis, (PCA)) which also successfully identifies the divergent behavior near criticality. Finally, we investigate the behavior of the previously mentioned concepts under a renormalization group coarse¬graining procedure, and present ideas for future research.