Low-temperature Glauber dynamics under weak competing interactions

Abstract

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.