Interaction potentials for mutually induced dipoles in uniform fields

TL;DR

This paper derives an improved interaction potential for mutually induced dipoles in uniform fields, incorporating many-body effects and providing an efficient computational scheme for large systems.

Contribution

It introduces a force-based derivation of the interaction potential that includes mutual induction effects and two- and three-body corrections, advancing modeling accuracy.

Findings

Classical dipole-dipole interactions are significantly altered by mutual induction.

Neglecting mutual magnetization leads to substantial errors in anisotropic assemblies.

An efficient iterative scheme enables accurate large-scale simulations.

Abstract

Dipolar interactions govern the structure and dynamics of many soft-matter systems, from molecular to colloids assemblies. When dipole moments are induced by an external field, mutual interactions lead to a many-body magnetization response that cannot be described by fixed-dipole models. Here, we derive the interaction potential for a system of mutually interacting induced dipoles in a uniform external field using a force-based approach. By accounting for the displacement-induced variation of the dipole moments, we obtain an interaction potential consisting of the classical dipole-dipole term supplemented by two- and three-body corrections arising from mutual induction. Comparisons with simplified models that neglect mutual magnetization reveal significant errors in the interaction potential, particularly in anisotropic particle assemblies. We also discuss an efficient $\mathcal{O}(N^2)$ iterative scheme for computing the mutual magnetization, enabling accurate simulations of large dipolar systems.