  Magnetic structure factor (MSF) is employed to investigate the ground state
degeneracy in rectangular-like artificial spin ices. Our analysis considers the
importance of nanoislands size via dumbbell model approximation. Pinch points
in MSF and residual entropy are found for rectangular lattices with
disconnected nanoislands, signalizing an emergent gauge field, through which
magnetic monopoles interact effectively. Dipole-dipole interaction is also used
and its predictions are compared with those obtained by dumbbell model.

Mesoscale and Nanoscale Physics