Dynamical scaling, domain-growth kinetics, and domain-wall shapes of quenched two-dimensional anisotropic XY models

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  • Ole G. Mouritsen
  • Eigil Praestgaard

The domain-growth kinetics in two different anisotropic two-dimensional XY-spin models is studied by computer simulation. The models have uniaxial and cubic anisotropy which leads to ground-state orderings which are twofold and fourfold degenerate, respectively. The models are quenched from infinite to zero temperature as well as to nonzero temperatures below the ordering transition. The continuous nature of the spin variables causes the domain walls to be soft and characterized by a finite thickness. The steady-state thickness of the walls can be varied by a model parameter, P. At zero temperature, the domain-growth kinetics is found to be independent of the value of this parameter over several decades of its range. This suggests that a universal principle is operative. The domain-wall shape is analyzed and shown to be well represented by a hyperbolic tangent function. The growth process obeys dynamical scaling and the shape of the dynamical scaling function pertaining to the structure factor is found to depend on P. Specifically, this function is described by a Porod-law behavior, q-, where increases with the wall softness. The kinetic exponent, which describes how the linear domain size varies with time, R(t)tn, is for both models at zero temperature determined to be n0.25, independent of P. At finite temperatures, the growth kinetics is found to cross over to the Lifshitz-Allen-Cahn law characterized by n0.50. The results support the idea of two separate zero-temperature universality classes for soft-wall and hard-wall kinetics, and furthermore suggest that these classes become identical at finite temperatures.

Original languageEnglish
JournalPhysical Review B (Condensed Matter and Materials Physics)
Issue number4
Pages (from-to)2703-2714
Number of pages12
Publication statusPublished - 1988
Externally publishedYes

ID: 238390255