Influence of thermal fluctuations on the geometry of the interfaces of the quenched Ising model

Abstract

We study the role of the quench temperature $T_f$ in the phase-ordering kinetics of the Ising model with single spin flip in $d=2,3$. Equilibrium interfaces are flat at $T_f=0$, whereas at $T_f>0$ they are curved and rough (above the roughening temperature in $d=3$). We show, by means of scaling arguments and numerical simulations, that this geometrical difference is important for the phase-ordering kinetics as well. In particular, while the growth exponent $z=2$ of the size of domains $L(t)\sim t^{1/z}$ is unaffected by $T_f$, other exponents related to the interface geometry take different values at $T_f=0$ or $T_f>0$. For $T_f>0$ a crossover phenomenon is observed from an early stage where interfaces are still flat and the system behaves as at $T_f=0$, to the asymptotic regime with curved interfaces characteristic of $T_f>0$. Furthermore, it is shown that the roughening length, although sub-dominant with respect to $L(t)$, produces appreciable correction to scaling up to very long times in $d=2$.

21 pages, 15 figures. To be published in Phys. Rev. E

References in corpus (4)

• Exact results for curvature-driven coarsening in two dimensions
• Domain growth morphology in curvature driven two dimensional coarsening
• Test of Local Scale Invariance from the direct measurement of the response function in the Ising model quenched to and to below $T_C$
• Aging dynamics and the topology of inhomogenous networks

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• Topological regulation of activation barriers on fractal substrates
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• Coarsening in 3D Nonconserved Ising Model at Zero Temperature: Anomalies in structure and relaxation of order-parameter autocorrelation
• Correlators in phase-ordering from Schrödinger-invariance
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• On a relation between roughening and coarsening
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