Identifying Phase Transitions with Machine Learning
Poster Number
12C
Format
Poster Presentation
Faculty Mentor Name
Kieran Holland
Faculty Mentor Department
Physics
Abstract/Artist Statement
The Ising Model is a mathematical model that represents interacting particles in a lattice, and is often used to model ferromagnetism in statistical mechanics. The model describes a system of particles with two possible spin states, and can be generalized by the Potts Model, which allows for q possible states. Machine Learning offers new methods for examining phase transitions intrinsic to mathematical models such as this. We write a collective Monte-Carlo cluster algorithm to generate independent spin configurations of the 2-dimensional Ising model, and test the effectiveness of this algorithm by validating the experimentally known critical exponents of the Ising Model that correspond to its phase transition. Independent configurations are used to train a Convolutional Neural Network, a specific Machine Learning architecture often used in image classification, to distinguish ordered and disordered states. This is used to determine the critical temperature at which the phase transition occurs for the model. Through a process called Transfer Learning, we examine Potts Model configurations using the Ising-trained Neural Network, in order to demonstrate the possible applications of Machine Learning in studying more complicated structures.
Location
Information Commons, William Knox Holt Memorial Library and Learning Center
Start Date
29-4-2023 10:00 AM
End Date
29-4-2023 1:00 PM
Identifying Phase Transitions with Machine Learning
Information Commons, William Knox Holt Memorial Library and Learning Center
The Ising Model is a mathematical model that represents interacting particles in a lattice, and is often used to model ferromagnetism in statistical mechanics. The model describes a system of particles with two possible spin states, and can be generalized by the Potts Model, which allows for q possible states. Machine Learning offers new methods for examining phase transitions intrinsic to mathematical models such as this. We write a collective Monte-Carlo cluster algorithm to generate independent spin configurations of the 2-dimensional Ising model, and test the effectiveness of this algorithm by validating the experimentally known critical exponents of the Ising Model that correspond to its phase transition. Independent configurations are used to train a Convolutional Neural Network, a specific Machine Learning architecture often used in image classification, to distinguish ordered and disordered states. This is used to determine the critical temperature at which the phase transition occurs for the model. Through a process called Transfer Learning, we examine Potts Model configurations using the Ising-trained Neural Network, in order to demonstrate the possible applications of Machine Learning in studying more complicated structures.