Riesch C, Radons G, Magerle R. Pathways to equilibrium orientation fluctuations in finite stripe-forming systems.
Phys Rev E 2018;
96:052224. [PMID:
29347679 DOI:
10.1103/physreve.96.052224]
[Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2017] [Indexed: 11/07/2022]
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 λ_{∥}^{*}(t) in the direction parallel to the stripes, which increases with time t as λ_{∥}^{*}(t)∼t^{1/4}. Simultaneously, the orientation correlation length ξ_{⊥}(t) in the direction perpendicular to the stripes increases as ξ_{⊥}(t)∼t^{1/2} [Riesch et al., Interface Focus 7, 20160146 (2017)2042-889810.1098/rsfs.2016.0146]. Here we show that finite systems of size L_{⊥}×L_{∥} with periodic boundary conditions reach equilibrium when the dominant modulation length λ_{∥}^{*}(t) reaches the system size L_{∥} in the stripe direction. The equilibration time τ_{eq}^{∥} is solely determined by L_{∥}, with τ_{eq}^{∥}∼L_{∥}^{4}. In systems with L_{⊥}<L_{∥}^{2}/2πλ_{p}, where λ_{p} is the undulation penetration length, the initial aging and coarsening dynamics changes at the crossover time τ_{C}^{⊥}∼L_{⊥}^{2} to an aging and coarsening dynamics described by the one-dimensional Mullins-Herring equation, before reaching equilibrium at τ_{∥}^{eq}. 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.
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