Emergent long-tailed dynamics in spin ice

In this study, we reveal long-tail dynamics spontaneously arising from a magnetic system. Specifically, we consider a classical spin system and demonstrate the emergence of a spin-ice physics when drive-induced heating is well suppressed. We show that at high driving frequencies, magnetic monopole excitations exhibit nonergodic stochastic dynamics characterized by power-law-distributed trapping times with long tails—a behavior that persists even in the absence of driving. At intermediate driving frequencies, the system eventually heats up to an infinite-temperature state. However, contrary to conventional wisdom of Floquet heating, the heating time in our model is extremely sensitive to different initial-state realizations and also follows a long-tailed power-law distribution, which arise specifically due to periodic driving. We show that an effective short-range attractive interaction between monopoles is responsible for the long-tailed distributions observed in both monopole and heating dynamics.