Low-temperature Glauber dynamics under weak competing interactions

We consider the low but nonzero-temperature regimes of the Glauber dynamics in a chain of Ising spins with first- and second-neighbor interactions J1,J2. For 0<-J2/|J1|<1 it is known that at T=0 the dynamics is both metastable and noncoarsening, while being always ergodic and coarsening in the limit of T→0+. Based on finite-size scaling analyses of relaxation times, here we argue that in that latter situation the asymptotic kinetics of small or weakly frustrated -J2/|J1| ratios is characterized by an almost ballistic dynamic exponent z≃1.03(2) and arbitrarily slow velocities of growth. By contrast, for noncompeting interactions the coarsening length scales are estimated to be almost diffusive.