Eur. Phys. J. B 81, 309-319 (2011)
https://doi.org/10.1140/epjb/e2011-20185-y

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

¹ Nanophysics Group, Department of Physics, Electric Engineering Faculty, CUJAE, Ave 114 final, La Habana, Cuba
² “Henri-Poincaré-Group” of Complex Systems, Physics Faculty, University of Havana, La Habana, CP, 10400, Cuba
³ Department of Theoretical Physics, Physics Faculty, University of Havana, La Habana, CP, 10400, Cuba
⁴ Dipartimento di Fisica, Università di Roma “La Sapienza”, P.le Aldo Moro 2, 00185 Roma, Italy
⁵ Departamento de Física, Universidade Federal do Rio Grande do Sul and National Institute of Science and Technology for Complex Systems CP 15051, 91501-970, Porto Alegre, Brasil

Corresponding author: ^a rogelio@electrica.cujae.edu.cu

Received: 10 March 2011
Published online: 7 June 2011

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.