Interplay between the charge transport phenomena and the charge-transfer phase transition in RbxMn[Fe(CN)6]y.zH2O

Charge transport and dielectric measurements were carried out on compacted powder and single-crystal samples of bistable RbxMn[Fe(CN)6]y·zH2O in the two valence-tautomeric forms (MnIIFeIII and MnIIIFeII) as a function of temperature (120-350 K) and frequency (10-2-106 Hz). The complex conductivity data reveal universal conductivity behavior and obey the Barton-Nakajima-Namikawa relationship. The charge transport is accompanied by dielectric relaxation that displays the same thermal activation energy as the conductivity. Surprisingly, the activation energy of the conductivity was found very similar in the two valence-tautomeric forms (0.55 eV), and the conductivity change between the two phases is governed mainly by the variation of the preexponential factor in each sample. The phase transition is accompanied by a large thermal hysteresis of the conductivity and the dielectric constant. In the hysteresis region, however, a crossover occurs in the charge transport mechanism at T < 220 K from an Arrhenius-type to a varying activation energy behavior, conferring an unusual “double-loop” shape to the hysteresis.

Unveiling temporal correlations characteristic of a phase transition in the output intensity of a fiber laser

We use advanced statistical tools of time-series analysis to characterize the dynamical complexity of the transition to optical wave turbulence in a fiber laser. Ordinal analysis and the horizontal visibility graph applied to the experimentally measured laser output intensity reveal the presence of temporal correlations during the transition from the laminar to the turbulent lasing regimes. Both methods unveil coherent structures with well-defined time scales and strong correlations both, in the timing of the laser pulses and in their peak intensities. Our approach is generic and may be used in other complex systems that undergo similar transitions involving the generation of extreme fluctuations.

Investigating optical complexity of the phase transition in the intensity of a fibre laser radiation

Fibre lasers have been shown to manifest a laminar-to-turbulent transition when increasing its pump power. In order to study the dynamical complexity of this transition we use advanced statistical tools of time-series analysis. We apply ordinal analysis and the horizontal visibility graph to the experimentally measured laser output intensity. This reveal the presence of temporal correlations during the transition from the laminar to the turbulent lasing regimes. Both methods allow us to unveil coherent structures with well defined time-scales and strong correlations both, in the timing of the laser pulses and in their peak intensities.

Laminar-turbulent transition in Raman fiber lasers:a first passage statistics based analysis

Loss of coherence with increasing excitation amplitudes and spatial size modulation is a fundamental problem in designing Raman fiber lasers. While it is known that ramping up laser pump power increases the amplitude of stochastic excitations, such higher energy inputs can also lead to a transition from a linearly stable coherent laminar regime to a non-desirable disordered turbulent state. This report presents a new statistical methodology, based on first passage statistics, that classifies lasing regimes in Raman fiber lasers, thereby leading to a fast and highly accurate identification of a strong instability leading to a laminar-turbulent phase transition through a self-consistently defined order parameter. The results have been consistent across a wide range of pump power values, heralding a breakthrough in the non-invasive analysis of fiber laser dynamics.

Threshold-induced phase transitions in perceptrons

Error rates of a Boolean perceptron with threshold and either spherical or Ising constraint on the weight vector are calculated for storing patterns from biased input and output distributions derived within a one-step replica symmetry breaking (RSB) treatment. For unbiased output distribution and non-zero stability of the patterns, we find a critical load, α p, above which two solutions to the saddlepoint equations appear; one with higher free energy and zero threshold and a dominant solution with non-zero threshold. We examine this second-order phase transition and the dependence of α p on the required pattern stability, κ, for both one-step RSB and replica symmetry (RS) in the spherical case and for one-step RSB in the Ising case.

Bulk and surface switching in Mn-Fe-based Prussian blue analogues

Many Prussian Blue Analogues are known to show a thermally induced phase transition close to room temperature and a reversible, photo-induced phase transition at low temperatures. This work reports on magnetic measurements, X-ray photoemission and Raman spectroscopy on a particular class of these molecular heterobimetallic systems, specifically on Rb0.81Mn[Fe(CN)6]0.95_1.24H2O, Rb0.97Mn[Fe(CN)6]0.98_1.03H2O and Rb0.70Cu0.22Mn0.78[Fe(CN)6]0.86_2.05H2O, to investigate these transition phenomena both in the bulk of the material and at the sample surface. Results indicate a high degree of charge transfer in the bulk, while a substantially reduced conversion is found at the sample surface, even in case of a near perfect (Rb:Mn:Fe=1:1:1) stoichiometry. Thus, the intrinsic incompleteness of the charge transfer transition in these materials is found to be primarily due to surface reconstruction. Substitution of a large fraction of charge transfer active Mn ions by charge transfer inactive Cu ions leads to a proportional conversion reduction with respect to the maximum conversion that is still stoichiometrically possible and shows the charge transfer capability of metal centers to be quite robust upon inclusion of a neighboring impurity. Additionally, a 532 nm photo-induced metastable state, reminiscent of the high temperature Fe(III)Mn(II) ground state, is found at temperatures 50-100 K. The efficiency of photo-excitation to the metastable state is found to be maximized around 90 K. The photo-induced state is observed to relax to the low temperature Fe(II)Mn(III) ground state at a temperature of approximately 123 K.

Interacting nonequilibrium systems with two temperatures

We investigate a simplified model of two fully connected magnetic systems maintained at different temperatures by virtue of being connected to two independent thermal baths while simultaneously being interconnected with each other. Using generating functional analysis, commonly used in statistical mechanics, we find exactly soluble expressions for their individual magnetization that define a two-dimensional nonlinear map, the equations of which have the same form as those obtained for densely connected equilibrium systems. Steady states correspond to the fixed points of this map, separating the parameter space into a rich set of nonequilibrium phases that we analyze in asymptotically high and low (nonequilibrium) temperature limits. The theoretical formalism is shown to revert to the classical nonequilibrium steady state problem for two interacting systems with a nonzero heat transfer between them that catalyzes a phase transition between ambient nonequilibrium states. © 2013 American Physical Society.

Self-sustained clusters and ergodicity breaking in spin models

Self-sustained spin clusters are analytically linked to ergodicity breaking in fully connected Ising and Sherrington-Kirkpatick (SK) models, relating the less understood spin space to the well understood state space. This correspondence is established through the absence of clusters in the paramagnetic phase, the presence of one dominant cluster in the Ising ferromagnet, and the formation of nontrivial clusters in SK spin glass. Yet unobserved phenomena are also revealed such as a first order phase transition in cluster sizes in the SK ferromagnet. The method could be adapted to investigate other spin models. © 2013 American Physical Society.

Self-organization in social tagging systems

Individuals often imitate each other to fall into the typical group, leading to a self-organized state of typical behaviors in a community. In this paper, we model self-organization in social tagging systems and illustrate the underlying interaction and dynamics. Specifically, we introduce a model in which individuals adjust their own tagging tendency to imitate the average tagging tendency. We found that when users are of low confidence, they tend to imitate others and lead to a self-organized state with active tagging. On the other hand, when users are of high confidence and are stubborn to change, tagging becomes inactive. We observe a phase transition at a critical level of user confidence when the system changes from one regime to the other. The distributions of post length obtained from the model are compared to real data, which show good agreement. © 2011 American Physical Society.

Langevin dynamics, large deviations and instantons for the quasi-geostrophic model and two-dimensional Euler equations

We investigate a class of simple models for Langevin dynamics of turbulent flows, including the one-layer quasi-geostrophic equation and the two-dimensional Euler equations. Starting from a path integral representation of the transition probability, we compute the most probable fluctuation paths from one attractor to any state within its basin of attraction. We prove that such fluctuation paths are the time reversed trajectories of the relaxation paths for a corresponding dual dynamics, which are also within the framework of quasi-geostrophic Langevin dynamics. Cases with or without detailed balance are studied. We discuss a specific example for which the stationary measure displays either a second order (continuous) or a first order (discontinuous) phase transition and a tricritical point. In situations where a first order phase transition is observed, the dynamics are bistable. Then, the transition paths between two coexisting attractors are instantons (fluctuation paths from an attractor to a saddle), which are related to the relaxation paths of the corresponding dual dynamics. For this example, we show how one can analytically determine the instantons and compute the transition probabilities for rare transitions between two attractors.