Dynamics of systems with isotropic competing interactions in an external field: a Langevin approach

TL;DR

This paper investigates the Langevin dynamics of a ferromagnetic system with competing interactions under an external field, combining analytical solutions and numerical simulations to understand aging and domain growth behaviors.

Contribution

It provides an analytical solution within the Hartree approximation and develops a numerical scheme to study isotropic competing interactions in an external field.

Findings

Confirmation of simple aging at zero temperature and field

Identification of a critical field $h_c$ affecting long-term dynamics

Logarithmic domain growth below $h_c$ not captured by the analytical model

Abstract

We study the Langevin dynamics of a ferromagnetic Ginzburg-Landau Hamiltonian with a competing long-range repulsive term in the presence of an external magnetic field. The model is analytically solved within the self consistent Hartree approximation for two different initial conditions: disordered or zero field cooled (ZFC), and fully magnetized or field cooled (FC). To test the predictions of the approximation we develop a suitable numerical scheme to ensure the isotropic nature of the interactions. Both the analytical approach and the numerical simulations of two-dimensional finite systems confirm a simple aging scenario at zero temperature and zero field. At zero temperature a critical field $h_c$ is found below which the initial conditions are relevant for the long time dynamics of the system. For $h < h_c$ a logarithmic growth of modulated domains is found in the numerical simulations but this behavior is not captured by the analytical approach which predicts a $t^1/2$ growth law at $T = 0$.