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PubMed1999

Orientational relaxation in Brownian rotors with frustrated interactions on a square lattice.

We present simulation results on the equilibrium relaxation of Brownian planar rotors based on a uniformly frustrated XY model on a square lattice. The rotational relaxation exhibits typical dynamic features of fragile supercooled liquids including the two-step relaxation. We observe a dynamic crossover from the high-temperature regime with Arrhenius behavior to the low-temperature regime with temperature-dependent activation energy. A consistent picture for the observed slow dynamics can be given in terms of the caging effect and thermal activation across potential barriers in the energy landscapes.

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PubMed2000

Behavior of frustrated phase in ferroelectric and antiferroelectric liquid crystalline mixtures.

Binary mixtures of two successive homologues from a series of 4-(4(')-alkoxy-biphenyl-4-yloxymethyl)benzoic acid 2-octanol esters exhibit a polar phase that differs from both ferroelectric (FE) and antiferroelectric (AF) phases, which exist in the pure compounds. When the concentration of the FE component is increased, this phase gradually changes its polar character from AF-like to FE-like, which is confirmed by the study of dielectric properties. Sample boundaries as well as the dc electric field introduce the FE phase, which remains stable after the field is switched off. Dielectric study confirms that this phase is composed of FE and AF clusters. The clusters arise due to frustration of FE and AF molecular order, which occurs as a result of the lowering of interlayer interactions.

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PubMed2000

Dynamics of the frustrated ising lattice gas

The dynamical properties of a three-dimensional model glass, the frustrated Ising lattice gas (FILG), are studied by Monte Carlo simulations. We present results of compression experiments, where the chemical potential is either slowly or abruptly changed, as well as simulations at constant density. One time quantities like density and two time quantities like correlations, responses, and mean square displacements are measured, and the departure from equilibrium clearly characterized. The aging scenario, particularly in the case of density autocorrelations, is reminiscent of spin glass phenomenology with violations of the fluctuation-dissipation theorem, typical of systems with one replica symmetry breaking. The FILG, as a valid on-lattice model of structural glasses, can be described with tools developed in spin glass theory and, being a finite-dimensional model, can open the way for a systematic study of activated processes in glasses.

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PubMed2000

Glass transition in the quenched and annealed version of the frustrated lattice gas model

In this paper we study the three-dimensional frustrated lattice gas model in the annealed version, where the disorder is allowed to evolve in time with a suitable kinetic constraint. Although the model does not exhibit any thermodynamic transition it shows a diverging peak at some characteristic time in the dynamical nonlinear susceptibility, similar to the results on the p-spin model in mean field and the Lennard-Jones mixture recently found by Donati et al. (e-print cond-mat/9905433). Comparing these results to those obtained in the model with quenched interactions, we conclude that the critical behavior of the dynamical susceptibility is reminiscent of the thermodynamic transition present in the quenched model, and signaled by the divergence of the static nonlinear susceptibility, suggesting therefore a similar mechanism also in supercooled glass-forming liquids.

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PubMed2000

Multiplicity of ordered phases in frustrated systems obtained from hard-spin mean-field theory

Random quenched dilution of the triangular-lattice antiferromagnetic Ising model locally relieves frustration, leading to ordering phenomena. We have studied this system, under such dilution of one sublattice, using hard-spin mean-field theory. After a threshold dilution, two sublattices develop nonzero magnetizations of equal magnitude and opposite signs, as all three sublattices exhibit spin-glass order. In this phase, multiple sets of ordered solutions occur. A phase diagram is obtained in dilution fraction and temperature.

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PubMed2001

Macroscopically frustrated Ising model.

A disordered spin-glass model in which both static and dynamical properties depend on macroscopic magnetizations is presented. These magnetizations interact via random couplings and, therefore, the typical quenched realization of the system exhibits a macroscopic frustration. The model is solved by using a revisited replica approach, and the broken symmetry solution turns out to coincide with the symmetric solution. Some dynamical aspects of the model are also discussed, showing how it could be a useful tool for describing some properties of real systems such as, for example, natural ecosystems or human social systems.

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PubMed2001

Monte Carlo study of the three-dimensional Coulomb frustrated Ising ferromagnet.

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.

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PubMed2001

Spin and density overlaps in the frustrated Ising lattice gas.

We perform large scale simulations of the frustrated Ising lattice gas, a three-dimensional lattice model of a structural glass, using the parallel tempering technique. We evaluate the spin and density overlap distributions, and the corresponding nonlinear susceptibilities, as a function of the chemical potential. We then evaluate the relaxation functions of the spin and density self-overlap, and study the behavior of the relaxation times. The results suggest that the spin variables undergo a transition very similar to the one of the Ising spin glass, while the density variables do not show any sign of transition at the same chemical potential. It may be that the density variables undergo a transition at a higher chemical potential, inside the phase where the spins are frozen.

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PubMed2002

Slow dynamics and aging in a nonrandomly frustrated spin system.

A simple, non-disordered spin model has been studied in an effort to understand the origin of the precipitous slowing down of dynamics observed in supercooled liquids approaching the glass transition. A combination of Monte Carlo simulations and exact calculations indicates that this model exhibits an entropy-vanishing transition accompanied by a rapid divergence of time scales. Measurements of various correlation functions show that the system displays a hierarchy of time scales associated with different degrees of freedom. Extended structures, arising from the frustration in the system, are identified as the source of the slow dynamics. In the simulations, the system falls out of equilibrium at a temperature T(g) higher than the entropy-vanishing transition temperature and the dynamics below T(g) exhibits aging as distinct from coarsening. The cooling rate dependence of the energy is also consistent with the usual glass formation scenario.

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PubMed2002

Langevin dynamics of the Coulomb frustrated ferromagnet: A mode-coupling analysis.

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.

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PubMed2002

Dynamics and thermodynamics of the spherical frustrated Blume-Emery-Griffiths model.

We introduce a spherical version of the frustrated Blume-Emery-Griffiths model and solve exactly the statics and the Langevin dynamics for zero particle-particle interaction (K=0). In this case the model exhibits an equilibrium transition from a disordered to a spin glass phase, which is always continuous for nonzero temperature. The same phase diagram results from the study of the dynamics. Furthermore, we note the existence of a nonequilibrium time regime in a region of the disordered phase, characterized by aging, as occurs in the glassy phase. Due to a finite equilibration time, the system displays in this region the pattern of interrupted aging.

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PubMed2002

Surface scaling analysis of a frustrated spring-network model for surfactant-templated hydrogels.

We propose and study a statistical-mechanical model, inspired by recent atomic force microscopy studies of the surface structures of crosslinked polymer gels into which voids are introduced through templating by surfactant micelles [M. Chakrapani et al., e-print cond-mat/0112255]. The gel is represented by a frustrated, triangular network of nodes connected by springs of random equilibrium lengths. The nodes represent crosslinkers, and the springs correspond to polymer chains. The boundaries are fixed at the bottom, free at the top, and periodic in the lateral direction. Voids are introduced by deleting a proportion of the nodes and their associated springs. The model is numerically relaxed to a representative local energy minimum, resulting in an inhomogeneous, "clumpy" bulk structure. The free top surface is defined at evenly spaced points in the lateral (x) direction by the height of the topmost spring, measured from the bottom layer, h(x). Its scaling properties are studied by calculating the root-mean-square surface width and the generalized increment correlation functions C(q)(x)=<|h(x(0)+x)-h(x(0))|(q)>. The surface is found to have a nontrivial scaling behavior on small length scales, with a crossover to scale-independent behavior on large scales. As the vacancy concentration approaches the site-percolation limit, both the crossover length and the saturation value of the surface width diverge in a manner that appears to be proportional to the bulk connectivity length. This suggests that a percolation transition in the bulk also drives a similar divergence observed in surfactant templated polyacrylamide gels at high surfactant concentrations.

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PubMed2002

Superluminal advanced transmission of X waves undergoing frustrated total internal reflection: the evanescent fields and the Goos-Hänchen effect.

A study of X waves undergoing frustrated total internal reflection at a planar slab is provided. This is achieved by choosing the spectral plane wave components of the incident X wave to fall on the upper interface at angles greater than the critical angle. Thus, evanescent fields are generated in the slab and the peak of the field tunneling through the slab appears to be transmitted at a superluminal speed. Furthermore, it is shown that for deep barrier penetration, the peak of the transmitted field emerges from the rear interface of the slab before the incident peak reaches the front interface. To understand this advanced transmission of the peak of the pulse, a detailed study of the behavior of the evanescent fields in the barrier region is undertaken. The difference in tunneling behavior between deep and shallow barrier penetrations is shown to be influenced by the sense of the Goos-Hänchen shift.

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PubMed2003

Corrections to scaling in two-dimensional dynamic XY and fully frustrated XY models.

With large-scale Monte Carlo simulations, we investigate the two-dimensional dynamic XY and fully frustrated XY models. Dynamic relaxation starting from a disordered or an ordered state is carefully analyzed. It is confirmed that there is a logarithmic correction to scaling for a disordered start, but a power-law correction for an ordered start. Rather accurate values of the static exponent eta and the dynamic exponent z are estimated.

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PubMed2004

Nature of slow dynamics in a minimal model of frustration-limited domains.

We present simulation results for the dynamics of a schematic model based on the frustration-limited domain picture of glass-forming liquids. These results are compared with approximate theoretical predictions analogous to those commonly used for supercooled liquid dynamics. Although model relaxation times increase by several orders of magnitude in a non-Arrhenius manner as a microphase separation transition is approached, the slow relaxation is in many ways dissimilar to that of a liquid. In particular, structural relaxation is nearly exponential in time at each wave vector, indicating that the mode-coupling effects dominating liquid relaxation are comparatively weak within this model. Relaxation properties of the model are instead well reproduced by the simplest dynamical extension of a static Hartree approximation. This approach is qualitatively accurate even for temperatures at which the mode-coupling approximation predicts loss of ergodicity. These results suggest that the thermodynamically disordered phase of such a minimal model poorly caricatures the slow dynamics of a liquid near its glass transition.

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PubMed2004

Self-assembled uniaxial and biaxial multilayer structures in chiral smectic liquid crystals frustrated between ferro- and antiferroelectricity.

With a view to obtain a molecular model for the subphases produced by the frustration between ferro- and antiferroelectricity in chiral smectic liquid crystals, we report results on two compounds and observe (i) the staircase character of uniaxial Sm C(*)(alpha) itself in the bulk and (ii) the multipeaked characteristic reflection bands due to the modulated helical structures just above the Sm C(*)(A) temperature range. We suggest the emergence of several uniaxial and biaxial subphases. The results show that both types of subphases can be specified by q(T) = [F] / ( [A] + [F] ) in the zero-order approximation; [A] and [F] are the numbers of antiferroelectric and ferroelectric orderings in the unit cell. We consider the basis of both types of subphases, particularly the description of the short-pitch helical structure of Sm C(*)(alpha), in terms of the molecular models so far proposed and emphasize the important role played by the discrete flexoelectric polarization.

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PubMed2004

Optical gratings formed in thin smectic films frustrated on a single crystalline substrate.

Through the combination of three different, complementary techniques (optical microscopy, x-ray diffraction and atomic force microscopy), we reveal the deformations inside thin smectic films frustrated between two interfaces imposing antagonistic anchorings. We study the model system, 4-n-octyl-4'-cyanobiphenyl (8CB) between MoS2 and air, which is characterized by the competition between homeotropic anchoring at air and planar unidirectional anchoring on the substrate, with thicknesses varying around 0.3 microm. Optical microscopy and x-ray diffraction demonstrate the continuous topology of smectic layers between the interfaces, which are stacked into periodic flattened hemicylinders. These latter are one-dimensional (1D) focal conic domains which form an optical grating in the smectic film, of a period ranging from 1 to 2.5 microm. The interpretation of our results through an energetic model, associated with the atomic force microscopy (AFM) measurements, shows the presence below a critical thickness of a new type of curvature wall between neighboring hemicylinders.

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PubMed2004

Epitaxial frustration in deposited packings of rigid disks and spheres.

We use numerical simulation to investigate and analyze the way that rigid disks and spheres arrange themselves when compressed next to incommensurate substrates. For disks, a movable set is pressed into a jammed state against an ordered fixed line of larger disks, where the diameter ratio of movable to fixed disks is 0.8. The corresponding diameter ratio for the sphere simulations is 0.7, where the fixed substrate has the structure of a (001) plane of a face-centered cubic array. Results obtained for both disks and spheres exhibit various forms of density-reducing packing frustration next to the incommensurate substrate, including some cases displaying disorder that extends far from the substrate. The disk system calculations strongly suggest that the most efficient (highest-density) packings involve configurations that are periodic in the lateral direction parallel to the substrate, with substantial geometric disruption occurring only near the substrate. Some evidence has also emerged suggesting that for the sphere systems a corresponding structure doubly periodic in the lateral directions would yield the highest packing density; however, all of the sphere simulations completed thus far produced some residual "bulk" disorder not obviously resulting from substrate mismatch. In view of the fact that the cases studied here represent only a small subset of all that eventually deserve attention, we end with discussion of the directions in which first extensions of the present simulations might profitably be pursued.

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