  We investigate the antiferromagnetically ordered state in the half-filled
Hubbard model on the Socolar dodecagonal tiling. When the interaction is
introduced, the staggered magnetizations suddenly appear, which results from
the existence of the macroscopically degenerate states in the tightbinding
model. The increase of the interaction strength monotonically increases the
magnetizations although its magnitude depends on the local environments.
Magnetization profile is discussed in the perpendicular space. The similarity
and difference are also addressed in magnetic properties in the Hubbard model
on the Penrose, Ammann-Beenker, and Socolar dodecagonal tilings.
