Vortex effects on domain growth: The clock model

The development of order in the clock (${\mathbf{Z}}_N$) model is studied following a quench from high temperature ($T\gg T_c$) to very low temperatures, where the system has a ferromagnetic ground state. We find that the mean domain size $R$ and energy $E$ do not increase algebraically with time, in contrast to the behavior observed for the $Q$-state Potts model. Instead, we find that quenched-in vortices, present even at low temperature, play an important role in the domain growth, ultimately pinning the growth for long times.