Dipolar Ising Model: Phases, Growth Laws and Universality

Abstract

The behavior of many magnetic and dielectric solids, and the more contemporary magnetic super-lattices, is governed by dipolar interactions. They are anisotropic and long-ranged, having varied consequences ranging from ground states with complicated magnetic order to the presence of glassy dynamics characterised by a plethora of relaxation times.These systems are well-captured by the dipolar Ising model (DIM) with nearest-neighbor exchange interactions (J) and long-range dipolar interactions (D). Depending on the relative interaction strength Γ =J/D, there are four phases of distinct magnetic order and symmetry. Using Monte Carlo simulations, we perform deep quenches to study domain growth or coarsening in the d= 3 DIM. This important non-equilibrium phenomenon has not been addressed as dipolar interactions are notoriously difficult to handle theoretically. Our study reveals that, in spite of the anisotropy in interactions and diversity in ground state configurations, we observe universality in the ordering dynamics of all phases.

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