Abstract
Small-angle orientation fluctuations in ordered stripe-forming systems free of topological defects can exhibit aging and anisotropic growth of two length scales. In infinitely extended systems, the stripe orientation field develops a dominant modulation length in the direction parallel to the stripes, which increases with time as . Simultaneously, the orientation correlation length in the direction perpendicular to the stripes increases as [Riesch et al., Interface Focus 7, 20160146 (2017)]. Here we show that finite systems of size with periodic boundary conditions reach equilibrium when the dominant modulation length reaches the system size in the stripe direction. The equilibration time is solely determined by , with . In systems with , where is the undulation penetration length, the initial aging and coarsening dynamics changes at the crossover time to an aging and coarsening dynamics described by the one-dimensional Mullins-Herring equation, before reaching equilibrium at . Our work reveals the two pathways to equilibrium in stripe phases with periodic boundary conditions, the finite-size scaling behavior of equilibrium orientation fluctuations, and the characteristic exponents associated with the influence of a finite system size.
4 More- Received 25 August 2017
DOI:https://doi.org/10.1103/PhysRevE.96.052224
©2017 American Physical Society