Rogelio Díaz-Méndez

H − T phase diagram of the two-dimensional Ising model with exchange and dipolar interactions

We explore the equilibrium properties of a two-dimensional Ising spin model with short-range exchange and long-range dipolar interactions as a function of the applied magnetic field

Non-Arrhenius relaxation of the Heisenberg model with dipolar and anisotropic interactions

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Asymptotic dynamics of a frustrated model with spherical constraint

. The model is studied through extensive Monte Carlo simulations that show the existence of many modulated phases with long-range orientational order for a wide range of fields. These phases are characterized by different wave vectors that change discontinuously with the magnetic field. In particular, the emergence of novel anharmonic phases that keep the orientational order but are characterized by several wave vectors is studied in detail. We provide numerical evidence supporting the existence of first-order transitions between modulated phases. At higher fields our results suggest a Kosterliz-Thouless scenario for the transition from a bubble to a ferromagnetic phase.

Monte Carlo simulations of the equilibrium and non-equilibrium properties of low-dimensional magnetic systems with long-range dipolar interactions

Abstract The dynamical properties of a 2D Heisenberg model with dipolar interactions and perpendicular anisotropy are studied using Monte Carlo simulations in two different ordered regions of the equilibrium phase diagram. We find a temperature defining a dynamical transition below which the relaxation suddenly slows down and the system apart from the typical Arrhenius relaxation to a Vogel–Fulcher–Tamann law. This anomalous behavior is observed in the scaling of the magnetic relaxation and may eventually lead to a freezing of the system. Through the analysis of the domain structures we explain this behavior in terms of the domains dynamics. Moreover, we calculate the energy barriers distribution obtained from the data of the magnetic viscosity. Its shape supports our comprehension of both, the Vogel–Fulcher–Tamann dynamical slowing down and the freezing mechanism.

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

We solve analytically the Langevin dynamics of the classic s pherical model considering the ferromagnetic exchange and a long-range antiferromagnetic interaction. Our results in the asymptotic regime, shows an equivalence in the functionality of the spatial and self-correla tions between this model and the recently studied Ginzburg-Landau frustrated model within the Hartree appro ximation. A careful discussion is done about the low temperature behavior in the context of glassy dynamics. The appearance of interesting features regarding the establishment of the ferromagnetic phase is also analyz ed in view of the effects of the spherical restriction. We propose a new variant of the spherical model in which the gl obal restriction is substituted by an infinite set of restrictions over finite size regions. This modification l eads to a new dynamical equation that suggests the appearance of the low temperature phase transition even in t he on-frustrated case were the classic spherical model fails.