Reconstruction of spin structures from topological charge distributions via generative neural network systems

TL;DR

This paper develops a generative neural network model incorporating physical and Fourier constraints to reconstruct microscopic spin configurations from macroscopic topological defect patterns, validated on the 2D XY model.

Contribution

It introduces an enhanced Wasserstein GAN with physical constraints to generate consistent spin configurations, advancing multiscale modeling of defect-rich spin systems.

Findings

Accurately reproduces magnetization, susceptibility, and correlations across temperatures.

Reveals limitations in modeling higher order energy fluctuations.

Uses topological data analysis to detect subtle differences near critical points.

Abstract

Localized topological defects inherently possess a multiscale character. While their microstructure configuration depends on the specific physical system, their topological features and mutual interactions can be described on the macroscale in terms of a particle representation. However, determining the physical properties associated with a given defect pattern often requires knowledge of the underlying microscopic structure. In this work, we extend a Wasserstein generative adversarial neural network by incorporating physical constraints and Fourier-space information to generate microscopic spin configurations consistent with prescribed macroscopic patterns and thermodynamic parameters. Using the two-dimensional XY model as a test case, where vortex-antivortex pairs act as long-range interacting defects, we show that the model generates spin configurations that accurately reproduce magnetization, susceptibility, helicity modulus, and spin-spin correlations over a wide range of temperatures below the Kosterlitz-Thouless transition. At the same time, deviations in the specific heat reveal limitations in reproducing higher order energy fluctuations. A complementary analysis based on topological data analysis uncovers subtle differences in global spin-correlation structures at near critical temperatures that are not apparent from conventional correlation functions alone. These results demonstrate both the promise and current limitations of generative approaches for multiscale studies of defect-dominated spin systems and at the same time highlight topological methods as valuable tools for characterizing critical behavior.