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1
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0000861193
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For reviews of scalar systems see, e.g., edited by, C. Domb, J. L. Lebowitz, Academic, New York
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(1983)
Phase Transitions and Critical Phenomena
, vol.8
, pp. 267
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Gunton, J.D.1
San Miguel, M.2
Sahni, P.S.3
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22
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84927504984
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and references therein.
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39
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84927505701
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Their results, on a nematic liquid crystal, correspond to n=2 of this paper.
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48
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0003672584
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edited by, A. J. McKane, M. Droz, J. Vannimenus, D. Wolf, (Plenum, New York, in press).
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Scale Invariance, Interfaces, and Non Equilibrium Dynamics
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Siegert, M.1
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52
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84927477099
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We use magnetic language throughout, but our results are not limited to magnetic systems.
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56
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84927488165
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Monte Carlo RG approaches citeRoland88 are not restricted to conserved systems. However, rather than predicting a particular growth law, they select the trial growth law that best reduces the data within an assumed fixed point structure.
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57
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4244001813
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Generically, an asymmetric potential will reduce the effective dimensionality of the order parameter, and can change the nature of defect cores. As long as there are multiple ground states (i.e., no effective magnetic field) our energy scaling approach applies, with n-1 equal to the effective dimensionality of the ground state manifold. In one dimensional scalar systems domain wall interactions dominate, so that anisotropies change the nature of the phase ordering process see
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(1994)
Phys. Rev. B
, vol.50
, pp. 9274
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Tutu, H.1
Fujisaka, H.2
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60
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84927485827
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Note, however, that the volume average magnitude of the order parameter is controlled primarily by the domain wall density for scalar systems, < 1- | φ| > sim L-1. For vector systems with defects (n leq d), at a distance r from the defect with ξ ll r ll L, one has 1 - | vecφ| sim ξ2/r2. This gives < 1- | vecφ| > sim L-2 ln(L/ξ) for n=2, and < 1- | vecφ| > sim L-2 for n>2.
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61
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84927460101
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One example is the 1D XY model citeNewman90a,Rutenberg94e.
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62
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84927470157
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We have assumed power law growth (with or without logarithmic factors) to obtain the time derivative scaling form from ( refEQN:TTSTRUCT).
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68
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84927488483
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The number density n(l) is defined by the total core volume density with a local length scale l divided by the expected core volume at that scale, ld-n. For point defects (n=d), n(l) is the coarse grained defect density distribution.
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74
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84927473591
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who used it in the context of Rayleigh Bénard convection.
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75
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84927493830
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For conserved scalar systems, a local ``effective mobility'' makes no sense, since the local movement of a domain wall changes the average order parameter.
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76
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84927458604
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Equation ( refEQN:2DXYFIELD) is an analytic solution to nabla2 theta =0 and hence represents a metastable configuration. The finite core size ξ, due to a finite V0 or a discrete lattice, destabilizes the configuration and leads to evolution. The finite rate of evolution then causes ( refEQN:2DXYFIELD) to break down at large distances from the vortices.
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90
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84927479842
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If there are no topological defects seeded by the initial conditions, then we expect L(t) sim t1/(σ+μ) for scaling systems.
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