Title: Slow Spin Dynamics and Self-Sustained Clusters in Sparsely Connected Systems,
Abstract: To identify emerging microscopic structures in low temperature spin glasses,
we study self-sustained clusters (SSC) in spin models defined on sparse random
graphs. A message-passing algorithm is developed to determine the probability
of individual spins to belong to SSC. Results for specific instances, which
compare the predicted SSC associations with the dynamical properties of spins
obtained from numerical simulations, show that SSC association identifies
individual slow-evolving spins. This insight gives rise to a powerful approach
for predicting individual spin dynamics from a single snapshot of an
equilibrium spin configuration, namely from limited static information, which
can be used to devise generic prediction tools applicable to a wide range of
areas.