ABSTRACT
We study the Langevin dynamics of the soft-spin, continuum version of the Coulomb-frustrated Ising ferromagnet. By using the dynamical mode-coupling approximation, supplemented by reasonable approximations for describing the equilibrium static correlation function, and the somewhat improved dynamical self-consistent screening approximation, we find that the system displays a transition from an ergodic to a nonergodic behavior. This transition is similar to that obtained in the idealized mode-coupling theory of glass-forming liquids and in the mean-field generalized spin glasses with one-step replica symmetry breaking. The significance of this result and the relation to the appearance of a complex free-energy landscape are also discussed.
ABSTRACT
We show by means of a Monte Carlo simulation study that three-dimensional models with long-range frustration display the generic phenomena seen in fragile glass-forming liquids. Due to their properties (absence of quenched disorder, physical motivation in terms of structural frustration, and tunable fragility), these systems appear as promising minimal theoretical models for describing the glass transition of supercooled liquids.
ABSTRACT
We have investigated, by Monte Carlo simulation, the phase diagram of a three-dimensional Ising model with nearest-neighbor ferromagnetic interactions and small, but long-range (Coulombic) antiferromagnetic interactions. We have developed an efficient cluster algorithm and used different lattice sizes and geometries, which allows us to obtain the main characteristics of the temperature-frustration phase diagram. Our finite-size scaling analysis confirms that the melting of the lamellar phases into the paramagnetic phase is driven first order by the fluctuations. Transitions between ordered phases with different modulation patterns are observed in some regions of the diagram, in agreement with a recent mean-field analysis.
ABSTRACT
We present a theoretical study of the phase diagram of a frustrated Ising model with nearest-neighbor ferromagnetic interactions and long-range (Coulombic) antiferromagnetic interactions. For nonzero frustration, long-range ferromagnetic order is forbidden, and the ground state of the system consists of phases characterized by periodically modulated structures. At finite temperatures, the phase diagram is calculated within the mean-field approximation. Below the transition line that separates the disordered and the ordered phases, the frustration-temperature phase diagram displays an infinite number of "flowers," each flower being made by an infinite number of modulated phases generated by structure combination branching processes. The specificities introduced by the long-range nature of the frustrating interaction and the limitation of the mean-field approach are finally discussed.
