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

ArXiv ID: 2504.19050 “View on arXiv”

Authors: Bruno Giorgio

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.

Keywords: Ising model, Monte Carlo method, volatility clustering, heavy tails, stylized facts, Equities (S&P 500)

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Lab Rats
• Why: The paper uses advanced statistical mechanics and agent-based modeling with Monte Carlo simulations, requiring high mathematical sophistication, but its empirical evaluation relies heavily on theoretical model fitting and visual comparisons to stylized facts rather than robust out-of-sample backtesting or trading performance metrics.

  flowchart TD
    A["Research Goal: Investigate Ising model<br>to replicate S&P 500 stylized facts"] --> B["Methodology: Monte Carlo Simulation"]
    B --> C["Data Input: S&P 500 Historical Data"]
    C --> D{"Computational Process:<br>Simulate Ising Model Phase Transitions"}
    D --> E["Key Outcomes: Model successfully replicates<br>Volatility Clustering, Heavy Tails, Negative Skewness,<br>Absence of Return Autocorrelation,<br>Presence of Absolute Return Autocorrelation"]