Complexity of magnetization and magnetic simplification

We use the Complexity=Volume (CV) prescription to study effect of a magnetic field on complexity formation for states in gauge theories dual two different gravitational models. In one these increases with intensity field, while other more interesting behavior is discovered, resulting phenomenon that we term simplification. The relevant difference between content second includes scalar operator non-vanishing vacuum expectation value. This leads us conclude direct impact increase state, but it can indirectly lower by diminishing associated additional degrees freedom when do not vanish across space. additionally compare results obtained working full ten dimensional backgrounds and their effective five truncations, exhibiting question still current about which surface, whether uplift 5D extremal hypersurface or surface 10D, should be used CV prescription.