Long-range Coulomb interactions and nonhydrodynamic behavior in thermal quenches in spin ice

When spin ice systems undergo a sudden thermal quench, they have been shown to enter long-lived metastable states where the monopole excitations form so-called noncontractible pairs [Phys. Rev. Lett. 104, 107201 (2010)]. While the nature of these states is well understood, the dynamical mechanisms underpinning their formation remain largely unexplored. We find that the long-range tail of the Coulomb interactions between monopoles plays a central role by suppressing the monopole-assisted decay of noncontractible pairs with respect to monopole–antimonopole annihilation. The existence of a transient, nonhydrodynamic regime allows the sytem to enter a metastable state whose lifetime can easily be astronomically large at low temperatures. We demonstrate this using Monte Carlo simulations and mean field population dynamics theory, and we provide an analytical understanding of the mechanisms at play. We derive the finite size scaling behavior of the density of noncontractible pairs in the plateau for both short- and long-range interactions and discuss the experimental implications of our results.