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Abstract:
In irreversible aggregation processes droplets or polymers of microscopic size successively coalesce until a large
cluster of macroscopic scale forms. This gelation transition is widely believed to be self-averaging, meaning that
the order parameter (the relative size of the largest connected cluster) attains well-defined values upon ensemble
averaging with no sample-to-sample fluctuations in the thermodynamic limit. Here, we report on anomalous
gelation transition types. Depending on the growth rate of the largest clusters, the gelation transition can show
very diverse patterns as a function of the control parameter, which includes multiple stochastic discontinuous
transitions, genuine non-self-averaging and ultraslow convergence of the transition point. Our framework may
be helpful in understanding and controlling gelation.
