TY - JOUR
T1 - Grain boundary pinning and glassy dynamics in stripe phases
AU - Boyer, Denis
AU - Viñals, Jorge
PY - 2002/4
Y1 - 2002/4
N2 - We study numerically and analytically the coarsening of stripe phases in two spatial dimensions, and show that transient configurations do not achieve long ranged orientational order but rather evolve into glassy configurations with very slow dynamics. In the absence of thermal fluctuations, defects such as grain boundaries become pinned in an effective periodic potential that is induced by the underlying periodicity of the stripe pattern itself. Pinning arises without quenched disorder from the nonadiabatic coupling between the slowly varying envelope of the order parameter around a defect, and its fast variation over the stripe wavelength. The characteristic size of ordered domains asymptotes to a finite value R g∼λ 0∈ -1/2exp(|a|/√∈), where ∈ ≪1 is the dimensionless distance away from threshold, λ 0 the stripe wavelength, and a a constant of order unity. Random fluctuations allow defect motion to resume until a new characteristic scale is reached, function of the intensity of the fluctuations. We finally discuss the relationship between defect pinning and the coarsening laws obtained in the intermediate time regime.
AB - We study numerically and analytically the coarsening of stripe phases in two spatial dimensions, and show that transient configurations do not achieve long ranged orientational order but rather evolve into glassy configurations with very slow dynamics. In the absence of thermal fluctuations, defects such as grain boundaries become pinned in an effective periodic potential that is induced by the underlying periodicity of the stripe pattern itself. Pinning arises without quenched disorder from the nonadiabatic coupling between the slowly varying envelope of the order parameter around a defect, and its fast variation over the stripe wavelength. The characteristic size of ordered domains asymptotes to a finite value R g∼λ 0∈ -1/2exp(|a|/√∈), where ∈ ≪1 is the dimensionless distance away from threshold, λ 0 the stripe wavelength, and a a constant of order unity. Random fluctuations allow defect motion to resume until a new characteristic scale is reached, function of the intensity of the fluctuations. We finally discuss the relationship between defect pinning and the coarsening laws obtained in the intermediate time regime.
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U2 - 10.1103/PhysRevE.65.046119
DO - 10.1103/PhysRevE.65.046119
M3 - Article
C2 - 12005938
AN - SCOPUS:41349104040
SN - 1539-3755
VL - 65
SP - 046119/1-046119/12
JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
IS - 4
M1 - 046119
ER -