Quenched Randomness, the Imry-Ma theorem, and Topology

In 1975, Imry and Ma made the analytical prediction that an exchange model in $d$ dimensions under the influence of a weak random field of strength $h_r$ will have a correlation length of $R_f \propto h_r^{-\frac{2}{4-d}}$ . However, numerical results since then have not given strong support to this analytical result. In our numerical studies, we have found that models that support topological structures, such as vortices or skyrmions, show spin states that have hysteresis, are highly dependent on initial conditions, and do not follow Imry-Ma prediction. Meanwhile, models that do not support these topological structures follow the Imry-Ma prediction, implying that the Imry-Ma state is not reached because of topological effects. These findings have implications for random magnets and flux lattices.