Disordered dipolar solids: Anisotropic growth laws and their slowing-down

Abstract

We use Monte Carlo simulations to study the kinetics of domain growth in the d = 3 random-field Ising model with dipolar interactions (RFIM+DI). This system models a large class of magnetic and dielectric solids. Our main results are as follows: i) The domains are anisotropic and elongated along the Ising (z) axis. The system exhibits generalized dynamical scaling with two distinct length scales and , where . However, the scaling function is not robust with respect to the disorder Δ. ii) For a fixed value of Δ, the interfaces are fractal with distinct fractal dimensions in the xy-plane and the z-direction. iii) The domain growth laws are also anisotropic, and exhibit distinct power laws on the time-scales of our simulations: and . iv) The exponents and have a simple dependence on Δ. Our results are novel and provide a fresh outlook to interpret experiments in disordered dipolar solids.

Impact of anisotropic interactions on nonequilibrium cluster growth at surfaces

“…14 (c). Moreover, we find that, as long as the cluster growth is isotropic, the scaling exponents have values g l ≈ g w ≈ 0.5, which are consistent with those observed during the domain growth in the random-field Ising model with isotropic interactions (RFIM-DI) [91] or the Axial Next-Nearest-Neighbor Ising Model (ANNNI) [92]. When anisotropy is switched on in the RFIM-DI and the ANNNI, the scaling exponents become different along the x-and y-direction, respectively.…”

Dipolar Ising Model: Phases, Growth Laws and Universality

“…In spite of its wide-ranging presence, there are only a few studies of the DIM in d = 3, and non-equilibrium phenomena are even less addressed [37,38]. This is primarily because handling long-ranged interactions is notoriously difficult, both analytically and computationally.…”