Machine learning of XY model on a spherical Fibonacci lattice

TL;DR

This paper investigates the XY model on a spherical Fibonacci lattice, demonstrating the existence of vortices, and develops machine learning methods to identify phases and vortex behaviors, with implications for space-based atomic gas experiments.

Contribution

It introduces a homogeneous spherical Fibonacci lattice for the XY model and applies machine learning techniques to analyze phase transitions and vortex dynamics.

Findings

Vortices are present in stable configurations on a sphere.

The machine learning model accurately predicts phase transition temperatures.

Clustering algorithms reveal vortex merging paths during simulations.

Abstract

We study the XY model on a spherical surface inspired by recently realized spherically confined atomic gases. Instead of a traditional latitude-longitude lattice, we introduce a much more homogeneous spherical lattice, the Fibonacci lattice, and use classical Monte Carlo simulations to determine spin configurations. The results clearly show that topological defects, in the form of vortices, must exist in the stable configuration on a sphere but vanish in a plane due to a mathematical theorem. Using these spin configurations as training samples, we propose a graph-convolutional-network based method to recognize different phases, and successfully predict the phase transition temperature. We also apply the density-based spatial clustering of applications with noise, a powerful machine learning algorithm, to monitor the merging path of two vortices with different topological charges on the sphere during Monte Carlo simulations. Our results provide reliable predictions for future space-based experiments on ultracold atomic gases confined on spherical lattice in the microgravity environment.