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The existence of topological solutions to the Chern–Simons model on lattice graphs

Bobo Hua, Genggeng Huang and Jiaxuan Wang
Vol. 19 (2026), No. 3, 485–504
DOI: 10.2140/apde.2026.19.485
Abstract

We prove the existence of topological solutions to the self-dual Chern–Simons model and the abelian Higgs system on the lattice graphs ℤn for n ≥ 2. This extends results of Huang, Lin and Yau (2020) from finite graphs to lattice graphs.

Keywords
topological solution, Chern–Simons model, exhaustion method, discrete isoperimetric inequality, lattice graphs
Mathematical Subject Classification
Primary: 35A01, 35A16, 35J91, 35R02
Milestones
Received: 20 April 2024
Accepted: 14 April 2025
Published: 11 March 2026
Authors
Bobo Hua
School of Mathematical Sciences, LMNS
Fudan University
Shanghai
China
Genggeng Huang
School of Mathematical Sciences, LMNS
Fudan University
Shanghai
China
Jiaxuan Wang
School of Mathematical Sciences
Fudan University
Shanghai
China
© 2026 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY).

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