Aplicação de redes de Boltzmann ao aprendizado não supervisionado do modelo de Ising 2D

Abstract

The purpose of this work is to study, through Machine Learning methods, the practical results obtained via programming applied to statistical physics models, in this case, the two-dimensional Ising model. Representative samples of the system were generated using a simulator based on the Wolff algorithm, covering different thermal regimes, with a primary focus on the critical region near the phase transition, considered here as Tc ≈ 2.3K. These samples were processed and used as input data for training stochastic generative models, specifically Restricted Boltzmann Machines (RBMs) and Deep Boltzmann Machines (DBMs). The training was carried out in an unsupervised manner, employing the contrastive divergence algorithm and Gibbs sampling. The DBMs, formed by stacking two RBMs, were used to reconstruct system samples and generate new synthetic configurations, known as fantasy particles. The results show that the models successfully learned and replicated statistical characteristics of the Ising system, such as domain formation and spatial patterns, particularly in the critical region. The application of machine learning models proved to be effective in representing and generating data from physical systems, suggesting a promising path for interdisciplinary studies bridging computational physics and artificial intelligence.