Domain Growth in Long-range Ising Models with Disorder

Abstract

Recent advances have highlighted the rich low-temperature kinetics of the long-range Ising model (LRIM). This study investigates domain growth in an LRIM with quenched disorder, following a deep low-temperature quench. Specifically, we consider an Ising model with interactions that decay as $J(r)\sim r^{-(D+\sigma )}$, where $D$ is the spatial dimension and $\sigma >0$ is the power-law exponent. The quenched disorder is introduced via random pinning fields at each lattice site. For nearest-neighbor models, we expect that domain growth during activated dynamics is logarithmic in nature: $R(t)\sim (\ln t{)}^{\alpha }$, with growth exponent $\alpha >0$. Here, we examine how long-range interactions influence domain growth with disorder in dimensions $D=1$ and $D=2$. In $D=1$, logarithmic growth is found to persist for various $\sigma >0$. However, in $D=2$, the dynamics is more complex due to the non-trivial interplay between extended interactions, disorder, and thermal fluctuations.

33 pages, 15 figures

References in corpus (28)

• Theory of Phase Ordering Kinetics
• Statistical mechanics and dynamics of solvable models with long-range interactions
• Growth Laws for Phase Ordering
• Phase Ordering Kinetics of One-Dimensional Non-Conserved Scalar Systems
• Domain Growth in Random Magnets
• Nonequilibrium dynamics of random field Ising spin chains: exact results via real space RG
• Crossover in Growth Law and Violation of Superuniversality in the Random Field Ising Model
• Random-field-like criticality in glass-forming liquids
• Upper and Lower Critical Decay Exponents of Ising Ferromagnets with Long-range Interaction
• Phase ordering kinetics of the long-range Ising model
• Aging in the long-range Ising model
• Growth Law and Superuniversality in the Coarsening of Disordered Ferromagnets
• Off equilibrium response function in the one dimensional random field Ising model
• Scaling and super-universality in the coarsening dynamics of the 3d random field Ising model
• Review of recent developments in the random-field Ising model
• One dimensional phase-ordering in the Ising model with space decaying interactions
• Kinetics of the Two-dimensional Long-range Ising Model at Low Temperatures
• Coarsening in inhomogeneous systems
• Zero-Temperature Coarsening in the Two-Dimensional Long-Range Ising Model
• Random-field Ising model criticality in a glass-forming liquid
• One-dimensional infinite component vector spin glass with long-range interactions
• Universality in the time correlations of the long-range 1d Ising model
• Coexistence of coarsening and mean field relaxation in the long-range Ising chain
• Asymptotic States of Ising Ferromagnets with Long-range Interactions
• Domain Growth and Aging in the Random Field XY Model: A Monte Carlo Study
• Ordering Dynamics of the Random Field Long-range Ising Model in One Dimension
• Ordering kinetics with long-range interactions: interpolating between voter and Ising models
• Existence of long-range order in random-field Ising model on Dyson hierarchical lattice