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

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 $T=0$.

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Cited by in corpus (4)

• Nature of Long-Range Order in Stripe-Forming Systems with Long-Range Repulsive Interactions
• On the mechanism behind the inverse melting in systems with competing interactions
• Melting of the two-dimensional solid phase in the Gaussian-core model
• The frustrated spherical model: an alternative to Ginzburg-Landau Hamiltonians with competing interactions