Microscopic origin of abrupt mixed-order phase transitions.

We suggest a possible origin for abrupt mixed-order transitions in physical systems and demonstrate it on three different Ising models with additional different types of interactions. We identify a plausible microscopic origin of this abrupt transition. It is driven by long-term microscopic cascades of changes in the underlying interaction network due to the additional interaction. These spontaneous cascades of microscopic changes accumulate over macroscopic time, resulting in a long-term metastable cascading plateau that ultimately causes an abrupt transition of the system. We also calculate the critical exponents for the cascading, magnetization, convergence slowing down, and the typical fluctuations of single-trajectory critical temperature and magnetization. The developed approach and our findings can shed light on the microscopic mechanism at the origin behind many abrupt transitions in nature and technology.