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 $J_1,, J_2$\mathrm{.}For$0 < -J_2 / | J_1 | < 1$itisknownthatat$T = 0$ the dynamics is both metastable and non-coarsening, while being always ergodic and coarsening in the limit of $T\to 0^{+}$. 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 $-J_2\mathrm{/}\mathrm{\mid }{J}_1\mathrm{\mid }$ ratios is characterized by an almost ballistic dynamic exponent $z\simeq 1.03(2)$ and arbitrarily slow velocities of growth. By contrast, for non-competing interactions the coarsening length scales are estimated to be almost diffusive.