Analysis unveils that conserving multipole moments in the Ising model leads to anomalous domain growth, suggesting new non-equilibrium universality classes.
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(t) ~ t1/2 in the absence of conserved quantities. When the order parameter is conserved, the domain growth slows to R(t) ~ t1/3. 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-th multipole moment causes domains to grow as R(t) ~ t1/(2m+3). This cascade of dynamical critical exponents characterizes a new family of non-equilibrium universality classes for fractonic systems.
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Gliozzi et al. (2025) studied this question.
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