Critical behaviors of filling-induced phase transitions in particle conserving east model and fracton systems

Filling-induced phase transitions have been founded in various kinetic constrained systems, where systems are governed by hydrodynamics in thermal phase and become completely frozen at low filling density. In this work, we investigate the filling-induced transition for a particle conserving east model and a fracton model. We reconcile the many different observed exponents, i.e., from the full counting statistics (FCS), autocorrelation functions, and individual block dynamics. In both models, the FCS is set by $z_{\textrm{crit}}$ in the usual way, while the autocorrelations are dominated by Griffiths rare region effects. In the fracton model, the growth of thermal blocks (in vacuum) exhibit two dynamical regimes, thermal and critical: at first the growth is bottlenecked by the need to redistribute particle density (while conserving dipole moment) before growing again; then, as the block approached critical density, its growth is governed by a new exponent which, although different from $z_{\textrm{crit}}$, fully determines the dynamical exponent at the critical point.