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 $d=2$.

arXiv comment21 pages, 15 figures. To be published in Phys. Rev. E

References in corpus (16)

• Theory of Phase Ordering Kinetics
• Off-equilibrium generalization of the fluctuation dissipation theorem for Ising spins and measurement of the linear response function
• Logarithmically slow domain growth in nonrandomly frustrated systems: Ising models with competing interactions
• Exact results for curvature-driven coarsening in two dimensions
• Domain growth morphology in curvature driven two dimensional coarsening
• On the connection between off-equilibrium response and statics in non disordered coarsening systems
• Interface fluctuations, bulk fluctuations and dimensionality in the off-equilibrium response of coarsening systems
• Scaling of the linear response function from zero field cooled and thermoremanent magnetization in phase ordering kinetics
• Persistence in higher dimensions : a finite size scaling study
• Scaling and universality in the aging kinetics of the two-dimensional clock model
• Phase-ordering kinetics on graphs
• Correction to scaling in the response function of the 2d kinetic Ising model
• 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
• Numerical Confirmation of Late-time t^{1/2} Growth in Three-dimensional Phase Ordering
• Defect Relaxation and Coarsening Exponents

Cited by in corpus (26)

• Kinetics of the Two-dimensional Long-range Ising Model at Low Temperatures
• Scaling in the Aging Dynamics of the Site-diluted Ising Model
• Effective mobility and diffusivity in coarsening processes
• Aging and Crossovers in Phase-Separating Fluid Mixtures
• Coexistence of coarsening and mean field relaxation in the long-range Ising chain
• Finite-Size Scaling Study of Aging during Coarsening in Non-Conserved Ising Model: The case of zero temperature quench
• Coarsening and percolation in the kinetic $2d$ Ising model with spin exchange updates and the voter model
• Fractality in Persistence Decay and Domain Growth during Ferromagnetic Ordering: Dependence upon initial correlation
• Relaxation in a Phase-separating Two-dimensional Active Matter System with Alignment Interaction
• Universal and non-universal features of the generalized voter class for ordering dynamics
• Slicing the $3d$ Ising model: critical equilibrium and coarsening dynamics
• The role of initial state and final quench temperature on the aging properties in phase-ordering kinetics
• Ordering Dynamics of the Random Field Long-range Ising Model in One Dimension
• Kinetics of Ferromagnetic Ordering in 3D Ising Model: Do we understand the case of zero temperature quench?
• Zero temperature coarsening in Ising model with asymmetric second neighbour interaction in two dimensions
• Topological regulation of activation barriers on fractal substrates
• Phase ordering in disordered and inhomogeneous systems
• Fractal character of the phase ordering kinetics of a diluted ferromagnet
• Superdiffusion-like behavior in zero-temperature coarsening of the $d=3$ Ising model
• Coarsening in 3D Nonconserved Ising Model at Zero Temperature: Anomalies in structure and relaxation of order-parameter autocorrelation
• Phase ordering in 3d disordered systems
• Heat exchanges in coarsening systems
• Aging following a zero-temperature quench in the $d=3$ Ising model
• Correlators in phase-ordering from Schrödinger-invariance
• A particle-based Ising model
• On a relation between roughening and coarsening