# Comparing Ising and Spin Glass Dynamics in Financial Markets: A Complex Systems Approach to Asset Interdependence

## TL;DR

This paper uses physics models to study how different assets in financial markets influence each other, showing that a more complex model better captures real-world market behavior.

## Contribution

The paper introduces a novel application of spin glass models to capture heterogeneous and nonlinear asset interactions in financial markets.

## Key findings

- Spin glass models reveal richer structural heterogeneity in financial markets compared to Ising models.
- Ising models serve as a benchmark for market coherence but miss nonlinear dependencies.
- Nonlinear mutual information provides more accurate coupling matrices for complex market interactions.

## Abstract

This paper analyzes financial market interdependence from a statistical-physics perspective by comparing Ising and spin glass representations of asset interactions. Financial markets are modeled as complex systems in which collective behavior emerges from time-varying interaction structures. Using daily data for a diversified 15-asset commodity system, including precious metals, energy commodities, industrial metals and soft commodities, over the period 2020–2024, we construct rolling coupling matrices based on both linear correlations and nonlinear mutual information and embed them into Ising and Sherrington–Kirkpatrick-type interaction frameworks. While aggregate synchronization indicators—such as average coupling strength and the largest eigenvalue—exhibit similar dynamics across the two representations, the spin glass framework reveals substantially richer structural heterogeneity. Preserving the sign structure of the interactions leads to wider dispersion, higher variability and nontrivial network configurations that are suppressed in the Ising representation. The results identify the Ising model as a benchmark for market coherence. The spin glass model is essential for capturing heterogeneous interactions and nonlinear dependence in financial markets.