Phase Transitions in Financial Markets Using the Ising Model: A Statistical Mechanics Perspective

Abstract: This dissertation investigates the ability of the Ising model to replicate statistical characteristics, or stylized facts, commonly observed in financial assets. The study specifically examines in the S&P500 index the following features: volatility clustering, negative skewness, heavy tails, the absence of autocorrelation in returns, and the presence of autocorrelation in absolute returns. A significant portion of the dissertation is dedicated to Ising model-based simulations. Due to the lack of an analytical or deterministic solution, the Monte Carlo method was employed to explore the model's statistical properties. The results demonstrate that the Ising model is capable of replicating the majority of the statistical features analyzed.