Subharmonics and aperiodicity in hysteresis loops

We show that it is possible to have hysteretic behavior for magnets that does not form simple closed loops in steady state, but cycles multiple times before returning to its initial state. We show this by studying the low temperature dynamics of the 3D Edwards-Anderson spin glass. The specific multiple varies from system to system and is often quite large and increases with system size. The last result suggests that the magnetization could be aperiodic in the large system limit for some realizations of randomness. It should be possible to observe this phenomenon experimentally.