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

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.