Dynamic Phase Transition in 2D Ising Systems: Effect of Anisotropy and Defects.

We investigate the dynamic phase transition in two-dimensional Ising models whose equilibrium characteristics are influenced by either anisotropic interactions or quenched defects. The presence of anisotropy reduces the dynamical critical temperature, leading to the expected result that the critical temperature approaches zero in the full-anisotropy limit. We show that a comprehensive understanding of the dynamic behavior of systems with quenched defects requires a generalized definition of the dynamic order parameter. By doing so, we demonstrate that the inclusion of quenched defects lowers the dynamic critical temperature as well, with a linear trend across the range of defect fractions considered. We also explore if and how it is possible to predict the dynamic behavior of specific magnetic systems with quenched randomness. Various geometric quantities, such as a defect potential index, the defect dipole moment, and the properties of the defect Delaunay triangulation, prove useful for this purpose.

Multistability in neural systems with random cross-connections.

Neural circuits with multiple discrete attractor states could support a variety of cognitive tasks according to both empirical data and model simulations. We assess the conditions for such multistability in neural systems using a firing rate model framework, in which clusters of similarly responsive neurons are represented as single units, which interact with each other through independent random connections. We explore the range of conditions in which multistability arises via recurrent input from other units while individual units, typically with some degree of self-excitation, lack sufficient self-excitation to become bistable on their own. We find many cases of multistability-defined as the system possessing more than one stable fixed point-in which stable states arise via a network effect, allowing subsets of units to maintain each others' activity because their net input to each other when active is sufficiently positive. In terms of the strength of within-unit self-excitation and standard deviation of random cross-connections, the region of multistability depends on the response function of units. Indeed, multistability can arise with zero self-excitation, purely through zero-mean random cross-connections, if the response function rises supralinearly at low inputs from a value near zero at zero input. We simulate and analyze finite systems, showing that the probability of multistability can peak at intermediate system size, and connect with other literature analyzing similar systems in the infinite-size limit. We find regions of multistability with a bimodal distribution for the number of active units in a stable state. Finally, we find evidence for a log-normal distribution of sizes of attractor basins, which produces Zipf's Law when enumerating the proportion of trials within which random initial conditions lead to a particular stable state of the system.

Stationary-State Statistics of a Binary Neural Network Model with Quenched Disorder.

In this paper, we study the statistical properties of the stationary firing-rate states of a neural network model with quenched disorder. The model has arbitrary size, discrete-time evolution equations and binary firing rates, while the topology and the strength of the synaptic connections are randomly generated from known, generally arbitrary, probability distributions. We derived semi-analytical expressions of the occurrence probability of the stationary states and the mean multistability diagram of the model, in terms of the distribution of the synaptic connections and of the external stimuli to the network. Our calculations rely on the probability distribution of the bifurcation points of the stationary states with respect to the external stimuli, calculated in terms of the permanent of special matrices using extreme value theory. While our semi-analytical expressions are exact for any size of the network and for any distribution of the synaptic connections, we focus our study on networks made of several populations, that we term "statistically homogeneous" to indicate that the probability distribution of their connections depends only on the pre- and post-synaptic population indexes, and not on the individual synaptic pair indexes. In this specific case, we calculated analytically the permanent, obtaining a compact formula that outperforms of several orders of magnitude the Balasubramanian-Bax-Franklin-Glynn algorithm. To conclude, by applying the Fisher-Tippett-Gnedenko theorem, we derived asymptotic expressions of the stationary-state statistics of multi-population networks in the large-network-size limit, in terms of the Gumbel (double exponential) distribution. We also provide a Python implementation of our formulas and some examples of the results generated by the code.

A Quenched Disorder in the Quantum-Critical Superconductor CeCoIn5.

Emergent inhomogeneous electronic phases in metallic quantum systems are crucial for understanding high-Tc superconductivity and other novel quantum states. In particular, spin droplets introduced by nonmagnetic dopants in quantum-critical superconductors (QCSs) can lead to a novel magnetic state in superconducting phases. However, the role of disorders caused by nonmagnetic dopants in quantum-critical regimes and their precise relation with superconductivity remain unclear. Here, the systematic evolution of a strong correlation between superconductive intertwined electronic phases and antiferromagnetism in Cd-doped CeCoIn5 is presented by measuring current-voltage characteristics under an external pressure. In the low-pressure coexisting regime where antiferromagnetic (AFM) and superconducting (SC) orders coexist, the critical current (Ic ) is gradually suppressed by the increasing magnetic field, as in conventional type-II superconductors. At pressures higher than the critical pressure where the AFM order disappears, Ic remarkably shows a sudden spike near the irreversible magnetic field. In addition, at high pressures far from the critical pressure point, the peak effect is not suppressed, but remains robust over the whole superconducting region. These results indicate that magnetic islands are protected around dopant sites despite being suppressed by the increasingly correlated effects under pressure, providing a new perspective on the role of quenched disorders in QCSs.

Enhancement of the magnetocaloric effect in geometrically frustrated cluster spin glass systems.

In this work, we theoretically demonstrate that a strong enhancement of the magnetocaloric effect is achieved in geometrically frustrated cluster spin-glass systems just above the freezing temperature. We consider a network of clusters interacting randomly which have triangular structure composed of Ising spins interacting antiferromagnetically. The intercluster disorder problem is treated using a cluster spin glass mean-field theory, which allows exact solution of the disordered problem. The intracluster part can be solved using exact enumeration. The coupling between the inter and intracluster problem incorporates the interplay between effects coming from geometric frustration and disorder. As a result, it is shown that there is the onset of cluster spin glass phase even with very weak disorder. Remarkably, it is exactly within a range of very weak disorder and small magnetic field that is observed the strongest isothermal release of entropy.

Observation of thickness-tuned universality class in superconducting ß-W thin films.

The interplay between quenched disorder and critical behavior in quantum phase transitions is conceptually fascinating and of fundamental importance for understanding phase transitions. However, it is still unclear whether or not the quenched disorder influences the universality class of quantum phase transitions. More crucially, the absence of superconducting-metal transitions under in-plane magnetic fields in 2D superconductors imposes constraints on the universality of quantum criticality. Here, we observe the thickness-tuned universality class of superconductor-metal transition by changing the disorder strength in ß-W films with varying thickness. The finite-size scaling uncovers the switch of universality class: quantum Griffiths singularity to multiple quantum criticality at a critical thickness of tc⊥1~8nm and then from multiple quantum criticality to single criticality at tc⊥2~16nm. Moreover, the superconducting-metal transition is observed for the first time under in-plane magnetic fields and the universality class is changed at tc‖~8nm. The observation of thickness-tuned universality class under both out-of-plane and in-plane magnetic fields provides broad information for the disorder effect on superconducting-metal transitions and quantum criticality.

Emergence of quenched disorder as a dominant control for complex phase diagram of rare-earth nickelates.

Competing interactions in complex materials tend to induce multiple quantum phases of comparable energetics close to the ground state stability. This requires novel strategies and tools to segregate such phases with desired control to manipulate the properties relevant for contemporary technologies. Here, we show 'quenched disorder (QD)' as a predominant control parameter to realize a broad range of the quantum phases of bulkRNiO3(R= rare-earth ion) phase diagram in a LaxEu1-xNiO3compounds by systematic introduction of QD. Using static and terahertz dynamic transport studies on epitaxial thin films, we demonstrate various phases such as Fermi to non-Fermi liquid crossover, bad metallic behavior, quantum criticality, preservation of orbital and charge order symmetry and increased electronic inhomogeneity responsible for Maxwell-Wagner type of dielectric response, etc. The underlying mechanisms are unveiled by the anomalous responses of microscopic quantities such as scattering rate, plasma frequency, spectral weight, effective mass, and disorder. The results and methodology implemented here can be a generic pursuit of disorder based unified control to extract quantum phases submerged in competing energetics in all complex materials.

Symmetry breaking and structure of a mixture of nematic liquid crystals and anisotropic nanoparticles.

Orientational ordering of a homogeneous mixture of uniaxial liquid crystalline (LC) molecules and magnetic nanoparticles (NPs) is studied using the Lebwohl-Lasher lattice model. We consider cases where NPs tend to be oriented perpendicularly to LC molecules due to elastic forces. We study domain-type configurations of ensembles, which are quenched from the isotropic phase. We show that for large enough concentrations of NPs the long range uniaxial nematic ordering is replaced by short range order exhibiting strong biaxiality. This suggests that the impact of NPs on orientational ordering of LCs for appropriate concentrations of NPs is reminiscent to the influence of quenched random fields which locally enforce a biaxial ordering.

Mathematical studies of the dynamics of finite-size binary neural networks: A review of recent progress.

Several mathematical approaches to studying analytically the dynamics of neural networks rely on mean-field approximations, which are rigorously applicable only to networks of infinite size. However, all existing real biological networks have finite size, and many of them, such as microscopic circuits in invertebrates, are composed only of a few tens of neurons. Thus, it is important to be able to extend to small-size networks our ability to study analytically neural dynamics. Analytical solutions of the dynamics of small-size neural networks have remained elusive for many decades, because the powerful methods of statistical analysis, such as the central limit theorem and the law of large numbers, do not apply to small networks. In this article, we critically review recent progress on the study of the dynamics of small networks composed of binary neurons. In particular, we review the mathematical techniques we developed for studying the bifurcations of the network dynamics, the dualism between neural activity and membrane potentials, cross-neuron correlations, and pattern storage in stochastic networks. Then, we compare our results with existing mathematical techniques for studying networks composed of a finite number of neurons. Finally, we highlight key challenges that remain open, future directions for further progress, and possible implications of our results for neuroscience.

Neural Field Models with Threshold Noise.

The original neural field model of Wilson and Cowan is often interpreted as the averaged behaviour of a network of switch like neural elements with a distribution of switch thresholds, giving rise to the classic sigmoidal population firing-rate function so prevalent in large scale neuronal modelling. In this paper we explore the effects of such threshold noise without recourse to averaging and show that spatial correlations can have a strong effect on the behaviour of waves and patterns in continuum models. Moreover, for a prescribed spatial covariance function we explore the differences in behaviour that can emerge when the underlying stationary distribution is changed from Gaussian to non-Gaussian. For travelling front solutions, in a system with exponentially decaying spatial interactions, we make use of an interface approach to calculate the instantaneous wave speed analytically as a series expansion in the noise strength. From this we find that, for weak noise, the spatially averaged speed depends only on the choice of covariance function and not on the shape of the stationary distribution. For a system with a Mexican-hat spatial connectivity we further find that noise can induce localised bump solutions, and using an interface stability argument show that there can be multiple stable solution branches.

Frustrated Solvation Structures Can Enhance Electron Transfer Rates.

Polar surfaces can interact strongly with nearby water molecules, leading to the formation of highly ordered interfacial hydration structures. This ordering can lead to frustration in the hydrogen bond network, and, in the presence of solutes, frustrated hydration structures. We study frustration in the hydration of cations when confined between sheets of the water oxidation catalyst manganese dioxide. Frustrated hydration structures are shown to have profound effects on ion-surface electron transfer through the enhancement of energy gap fluctuations beyond those expected from Marcus theory. These fluctuations are accompanied by a concomitant increase in the electron transfer rate in Marcus's normal regime. We demonstrate the generality of this phenomenon-enhancement of energy gap fluctuations due to frustration-by introducing a charge frustrated XY model, likening the hydration structure of confined cations to topological defects. Our findings shed light on recent experiments suggesting that water oxidation rates depend on the cation charge and Mn-oxidation state in these layered transition metal oxide materials.