Clasificación de configuraciones del modelo de Ising en dos y tres dimensiones mediante redes neuronales convolucionales : Redes neuronales artificiales para el estudio de los sistemas complejos.

Abstract

A Convolutional Neural Network (CNN) is a widely used deep learning tool for processing and classifying images. In physics, a system of interest is the Ising model, which is widely used for studying phase transition phenomena in magnetic materials. This model consists of a network of spins organized in space. The spatial distribution of the spins leads to the formation of visual patterns characterized by regions where they exhibit a specific orientation. This distribution varies depending on whether the system is two-dimensional or three-dimensional. Distinguishing between the patterns formed by both distributions is not easily discernible to the naked eye. The aim of this project is to determine whether the system described by the Ising model is two-dimensional or three-dimensional based on these patterns, regardless of whether it is in a steady state or in a transient regime. A CNN is employed to classify images of these patterns, generated through Monte Carlo simulations of a two and three-dimensional Ising model. The network is capable of classifying these patterns with remarkable effectiveness for states sufficiently distant from a random state, suggesting that it is possible to determine the dimensionality of the system from these patterns.