Monte Carlo Simulations of the Spin Vorticity Model on the Pyrochlore Lattice

Nearest-neighbor spin ice (NNSI) has been central to the study of frustrated magnetism for nearly thirty years, providing a framework that reveals emergent gauge fields and monopole excitations within geometrically frustrated spins on a pyrochlore lattice. From a coarse-grained vector field perspective, these spins obey a zero-divergence condition at the diamond lattice sites, effectively forming a Gauss law. By reversing this constraint and imposing a zero-curl condition on the spins – akin to an effective Ampere's law – the recently introduced spin vorticity model (SVM) is obtained.

In contrast to the point-like excitations within NNSI, the SVM features string-like excitations, analogous to closed current loops. Through Monte Carlo simulations which incorporate these excitations with zero-energy moves, we find that the SVM displays signatures of a spin liquid on the pyrochlore lattice, including extensive entropy and characteristic pinch points, while also undergoing a weak symmetry-breaking phase transition, with a small percentage of the system developing long-range order, signaled by weak magnetic Bragg peaks. We explore the underlying mechanisms behind this combination of phenomena, providing deeper insights into the physics of the SVM.