Study of Critical Phenomena with Monte Carlo and Machine Learning Techniques

Dynamical properties of non-equilibrium systems, similar to equilibrium ones, have been shown to obey robust time scaling laws which have enriched the concept of physical universality classes. In the first part of this Dissertation, we present the results of our investigations of some of the critical dynamical properties of systems belonging to the Voter or the Directed Percolation (DP) universality class. To be more precise, we focus on the aging properties of two-state and three-state Potts models with absorbing states and we determine temporal scaling of autocorrelation and autoresponse functions.

We propose a novel microscopic model which exhibits non-equilibrium critical points belonging to the Voter, DP and Ising Universality classes. We argue that our model has properties similar to the Generalized Voter Model (GVM) in its Langevin description. Finally, we study the time evolution of the width of interfaces separating different absorbing states.

The second part of this Dissertation is devoted to the applications of Machine Learning models in physical systems. First, we show that a trained Convolutional Neural Network (CNN) using configurations from the Ising model with conserved magnetization is able to find the location of the critical point. Second, using as our training dataset configurations of Ising models with conserved or non-conserved magnetization obtained in importance sampling Monte Carlo simulations, we investigate the physical properties of configurations generated by the Restricted Boltzmann Machine (RBM) model.

The first part of this research was sponsored by the US Army Research Office and was accomplished under Grant Number W911NF-17-1-0156.

The second part of this work was supported by the United States National Science Foundation through grant DMR-1606814.