Topological Order Generated by a Random Field in a 2D Exchange Model

We study a 2D exchange model with a weak static random field on lattices containing over 10⁸ spins. Ferromagnetic correlations persist on the Imry-Ma scale inversely proportional to the random-field strength and decay exponentially at greater distances. We find that the average energy of the correlated area is close to the ground-state energy of a Skyrmion, while the topological charge of the area is close to ±1. The correlation function of the topological charge density changes sign at a distance determined by the ferromagnetic correlation length, while its Fourier transform exhibits a maximum. These findings suggest that static randomness transforms a 2D ferromagnetic state into a Skyrmion-anti-Skyrmion glass.