Graph Neural Network Approach to Predicting Magnetization in Quasi-One-Dimensional Ising Systems

TL;DR

This paper introduces a graph neural network framework that predicts magnetic properties of quasi-one-dimensional Ising systems directly from their structure, accurately capturing key features and reducing computational costs.

Contribution

It is the first to apply GNNs to predict magnetization in Ising systems, effectively encoding lattice geometry and inferring magnetic behavior from structural connectivity.

Findings

Accurately reproduces magnetization curves including plateaus and critical points

Captures effects of geometric frustration and global symmetries

Reduces reliance on Monte Carlo simulations for predictions

Abstract

We present a graph-based deep learning framework for predicting the magnetic properties of quasi-one-dimensional Ising spin systems. The lattice geometry is encoded as a graph and processed by a graph neural network (GNN) followed by fully connected layers. The model is trained on Monte Carlo simulation data and accurately reproduces key features of the magnetization curve, including plateaus, critical transition points, and the effects of geometric frustration. It captures both local motifs and global symmetries, demonstrating that GNNs can infer magnetic behavior directly from structural connectivity. The proposed approach enables efficient prediction of magnetization without the need for additional Monte Carlo simulations.