Chaos is an important characterization of classical dynamical
systems. How is chaos linked to the long-time dynamics of collective
modes across phases and phase transitions? We address this by studying
chaos across Ising and Kosterlitz-Thouless transitions in classical XXZ
model. We show that spatio-temporal chaotic properties have crossovers
across the transitions and distinct temperature dependence in the high
and low-temperature phases which show normal and anomalous diffusions,
respectively. Our results also provide new insights into the dynamics of
interacting quantum systems in the semiclassical limit.
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