Condensed Matter

In the literature the most frequently cited data are quite contradictory, and there is no consensus on the global minimum value of 2D Edwards-Anderson (2D EA) Ising model. By means of computer simulations, with the help of exact polynomial Schraudolph-Kamenetsky algorithm, we examined the global minimum depth in 2D EA-type models. We found a dependence of the global minimum depth on the dimension of the problem N and obtained its asymptotic value in the limit N→∞ . We believe these evaluations can be further used for examining the behavior of 2D Bayesian models often used in machine learning and image processing.

Inverse statistical physics aims at inferring models compatible with a set of empirical averages estimated from a high-dimensional dataset of independently distributed equilibrium configurations of a given system. However, in several applications such as biology, data result from stochastic evolutionary processes, and configurations are related through a hierarchical structure, typically represented by a tree, and therefore not independent. In turn, empirical averages of observables superpose intrinsic signal related to the equilibrium distribution of the studied system and spurious historical (or phylogenetic) signal resulting from the structure underlying the data-generating process. The naive application of inverse statistical physics techniques therefore leads to systematic biases and an effective reduction of the sample size. To advance on the currently open task of extracting intrinsic signals from correlated data, we study a system described by a multivariate Ornstein-Uhlenbeck process defined on a finite tree. Using a Bayesian framework, we can disentangle covariances in the data corresponding to their multivariate Gaussian equilibrium distribution from those resulting from the historical correlations. Our approach leads to a clear gain in accuracy in the inferred equilibrium distribution, which corresponds to an effective two- to fourfold increase in sample size.

We perform numerical simulations of a long-range spherical spin glass with two and three body interaction terms. We study the gradient descent dynamics and the inherent structures found after a quench from initial conditions, well thermalized at temperature T in . In large systems, the dynamics strictly agrees with the integration of the mean-field dynamical equations. In particular, we confirm the existence of an onset initial temperature, within the liquid phase, below which the energy of the inherent structures undoubtedly depends on T in . This behavior is in contrast with that of pure models, where there is a 'threshold energy' that attracts all the initial configurations in the liquid. Our results strengthen the analogy between mean-field spin glass models and supercooled liquids.

A two-dimensional (2D) spin-1/2 antiferromagnetic Heisenberg model with a specific kind of quenched disorder is investigated, using the first principles nonperturbative quantum Monte Carlo calculations (QMC). The employed disorder distribution has a tunable parameter p which can be considered as a measure of the corresponding randomness. In particular, when p=0 the disordered system becomes the clean one. Through a large scale QMC, the dynamic critical exponents z , the ground state energy densities E 0 , as well as the Wilson ratios W of various p are determined with high precision. Interestingly, we find that the p dependence of z and W are likely to be complementary to each other. For instance, while the z of 0.4≤p≤0.9 match well among themselves and are statistically different from z=1 which corresponds to the clean system, the W for p<0.7 are in reasonable good agreement with that of p=0 . The technical subtlety of calculating these physical quantities for a disordered system is demonstrated as well. The results presented here are not only interesting from a theoretical perspective, but also can serve as benchmarks for future related studies.

An important but little-studied property of spin glasses is the stability of their ground states to changes in one or a finite number of couplings. It was shown in earlier work that, if multiple ground states are assumed to exist, then fluctuations in their energy differences --- and therefore the possibility of multiple ground states --- are closely related to the stability of their ground states. Here we examine the stability of ground states in two models, one of which is presumed to have a ground state structure that is qualitatively similar to other realistic short-range spin glasses in finite dimensions.

Advances in predictive modeling across multiple disciplines have yielded generative models capable of high veracity in predicting macroscopic functional responses of materials. Correspondingly, of interest is the inverse problem of finding the model parameter that will yield desired macroscopic responses, such as stress-strain curves, ferroelectric hysteresis loops, etc. Here we suggest and implement a Gaussian Process based methods that allow to effectively sample the degenerate parameter space of a complex non-local model to output regions of parameter space which yield desired functionalities. We discuss the specific adaptation of the acquisition function and sampling function to make the process efficient and balance the efficient exploration of parameter space for multiple possible minima and exploitation to densely sample the regions of interest where target behaviors are optimized. This approach is illustrated via the hysteresis loop engineering in ferroelectric materials, but can be adapted to other functionalities and generative models. The code is open-sourced and available at [this http URL].

Although quantum phase transitions involved with Anderson localization had been investigated for more than a half century, the role of spin polarization in these metal-insulator transitions has not been clearly addressed as a function of both the range of interactions and energy scales. Based on the Anderson-Hartree-Fock study, we reveal that the spin polarization has nothing to do with Anderson metal-insulator transitions in three dimensions as far as effective interactions between electrons are long-ranged Coulomb type. On the other hand, we find that metal-insulator transitions appear with magnetism in the case of Hubbard-type local interactions. In particular, we show that the multifractal spectrum of spin ↑ electrons differs from that of spin ↓ at the high-energy mobility edge, which indicates the existence of spin-dependent universality classes for metal-insulator transitions. One of the most fascinating and rather unexpected results is the appearance of half metals at intermediate energy scales above the high-energy mobility edge in Anderson-type insulators of the Fermi energy, that is, only spin ↑ electrons are delocalized while spin ↓ electrons are Anderson-type localized.

Nanowire networks (NWNs) represent a unique hardware platform for neuromorphic information processing. In addition to exhibiting synapse-like resistive switching memory at their cross-point junctions, their self-assembly confers a neural network-like topology to their electrical circuitry, something that is impossible to achieve through conventional top-down fabrication approaches. In addition to their low power requirements, cost effectiveness and efficient interconnects, neuromorphic NWNs are also fault-tolerant and self-healing. These highly attractive properties can be largely attributed to their complex network connectivity, which enables a rich repertoire of adaptive nonlinear dynamics, including edge-of-chaos criticality. Here, we show how the adaptive dynamics intrinsic to neuromorphic NWNs can be harnessed to achieve transfer learning. We demonstrate this through simulations of a reservoir computing implementation in which NWNs perform the well-known benchmarking task of Mackey-Glass (MG) signal forecasting. First we show how NWNs can predict MG signals with arbitrary degrees of unpredictability (i.e. chaos). We then show that NWNs pre-exposed to a MG signal perform better in forecasting than NWNs without prior experience of an MG signal. This type of transfer learning is enabled by the network's collective memory of previous states. Overall, their adaptive signal processing capabilities make neuromorphic NWNs promising candidates for emerging real-time applications in IoT devices in particular, at the far edge.

The vibrational anomalies of glasses, in particular the boson peak, are addressed from the standpoint of heterogeneous elasticity, namely the spatial fluctuations of elastic constants caused by the structural disorder of the amorphous materials. In the first part of this review article a mathematical analogy between diffusive motion in a disordered environment and a scalar simplification of vibrational motion under the same condition is emploited. We demonstrate that the disorder-induced long-time tails of diffusion correspond to the Rayleigh scattering law in the vibrational system and that the cross-over from normal to anomalous diffusion corresponds to the boson peak. The anomalous motion arises as soon as the disorder-induced self-energy exceeds the frequency-independent diffusivity/elasticity. For this model a variational scheme is emploited for deriving two mean-field theories of disorder, the self-consistent Born approximation (SCBA) and coherent-potential approximation (CPA). The former applies if the fluctuations are weak and Gaussian, the latter applies for stronger and non-Gaussian fluctuations. In the second part the vectorial theory of heterogenous elasticity is presented and solved in SCBA and CPA, introduced for the scalar model. Both approaches predict and explain the boson-peak and the associated anomalies, namely a dip in the acoustic phase velocity and a characteristic strong increase of the acoustic attenuation below the boson peak. Explicit expressions for the density of states and the inelastic Raman, neutron and X-ray scattering laws are given. Recent conflicting ways of explaining the boson-peak anomalies are discussed.

In d>2 dimensional, homogeneous threshold models discontinuous transition occur, but the mean-field solution provides 1/t power-law activity decay and other power-laws, thus it is called mixed-order or hybrid type. It has recently been shown that the introduction of quenched disorder rounds the discontinuity and second order phase transition and Griffiths phases appear. Here we provide numerical evidence, that even in case of high graph dimensional hierarchical modular networks the Griffiths phase of the K=2 threshold model is present below the hybrid phase transition. This is due to the fragmentation of the activity propagation by modules, which are connected via single links. This provides a widespread mechanism in case of threshold type of heterogeneous systems, modeling the brain or epidemics for the occurrence of dynamical criticality in extended Griffiths phase parameter spaces. We investigate this in synthetic modular networks with and without inhibitory links as well as in the presence of refractory states.