Recent experiments have demonstrated that it is possible to create macroscopic-ordered one- and two-dimensional nanostructures on (111) noble metal surfacs exploiting long-range substrate-mediated interaction. Here, we report on the systematic theoretical studies of magnetic properties of these atomic structures in the externally applied magnetic field. The spin dynamics is investigated by means of the kinetic Monte Carlo method based on transition-state theory. For the characteristic values of (i) magnetic anistropy energy of adatoms and (ii) exchange coupling between adatoms in the considered class of nanostrucures, we reveal the hysteresis-like behavior at low temperatures (typically at 1-3 K).