We study the dynamics of domain growth when multipole moments of the order parameter are conserved. Following a quench into the ordered phase of the Ising model, the typical size of domains grows with time as $R\left(t\right)\sim t^{1/2}$ in the absence of conserved quantities. When the order parameter is conserved, the domain growth slows to $R\left(t\right)\sim t^{1/3}$. Conservation of higher moments of the order parameter fundamentally modifies this behavior: Coarsening proceeds via anomalously slow growth. We analytically and numerically show that conservation of the $m\mathrm{th}$ multipole moment causes domains to grow as $R\left(t\right)\sim t^{1/(2m+3)}$. This cascade of dynamical critical exponents characterizes a new family of nonequilibrium universality classes for fractonic systems.

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• Fractons
• Nonequilibrium statistical mechanics
• Phase separation