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The athermal quasistatic (AQS) method is a powerful technique to study the mechanical behavior of disordered systems. However, its applicability is limited to temperatures near zero, where thermal activation is unlikely.
In a recent preprint by Kiefer-Emmanouilidis, Unanyan, Fleischhauer and Sirker [<a href="https://arxiv.org/abs/2203.06689" data-arxiv-id="2203.06689" class="link-https">arXiv:2203.06689</a>] the authors comment on our work which studied the number entropy in strongly disordered systems. The data presented in the comme...
We calculated numerically the localization length of one-dimensional Anderson model with correlated diagonal disorder. For zero energy point in the weak disorder limit, we showed that the localization length changes continuously as the correlation of the disorder increases.
We use the local load sharing fiber bundle model to demonstrate a shielding effect where strong fibers protect weaker ones. This effect exists due to the local stress enhancement around broken fibers in the local load sharing model, and it is therefore not present in the equal load sharing model.
We study the $\pm J$ SK model for small $N$'s up to $N=9$. We sort the $2^{N(N-1)/2}$ possible realizations of the coupling matrix into equivalence classes according to the gauge symmetry and permutation symmetry and determine the energy spectra for each of these classes.
We normalize the combinatorial Laplacian of a graph by the degree sum, look at its eigenvalues as a probability distribution and then study its Shannon entropy. Equivalently, we represent a graph with a quantum mechanical state and study its von Neumann entropy.
We investigate the localization properties of a quasi-one-dimensional two-channel system with symmetric and asymmetric onsite energies using the Aubry-André model. By analyzing the Lyapunov exponent and localization length, we characterize the phase transitions and critical behavior of the system.
In Generalized Linear Estimation (GLE) problems, we seek to estimate a signal that is observed through a linear transform followed by a component-wise, possibly nonlinear and noisy, channel. In the Bayesian optimal setting, Generalized Approximate Message Passing (GAMP) is known to achieve optimal performance for GLE....
We study both analytically, using the renormalization group (RG) to two loop order, and numerically, using an exact polynomial algorithm, the disorder-induced glass phase of the two-dimensional XY model with quenched random symmetry-breaking fields and without vortices. In the super-rough glassy phase, i.e. below the ...
We present a perturbative approach to disordered systems in one spatial dimension that accesses the full range of phase disorder and clarifies the connection between localization and phase information. We consider a long chain of identically disordered scatterers and expand in the reflection strength of any individual...
This thesis includes analysis of disordered spin ensembles corresponding to Exact Cover, a multi-access channel problem, and composite models combining sparse and dense interactions. The satisfiability problem in Exact Cover is addressed using a statistical analysis of a simple branch and bound algorithm.
We study the partition-function zeros in mean-field spin-glass models. We show that the replica method is useful to find the locations of zeros in a complex parameter plane.
We study the Lebwohl-Lasher model for systems in which spin are arranged on random graph lattices. At equilibrium our analysis follows the theory of spin-systems on random graphs which allows us to derive exact bifurcation conditions for the phase diagram.
We study correlations of atomic density in a weakly interacting Bose-Einstein condensate, expanding diffusively in a random potential. We show that these correlations are long-range and that they are strongly enhanced at long times.
We extend the self-consistent Ornstein-Zernike approximation (SCOZA), first formulated in the context of liquid-state theory, to the study of the random field Ising model. Within the replica formalism, we treat the quenched random field as an annealed spin variable, thereby avoiding the usual average over the random f...
Although the spectra of random networks have been studied for a long time, the influence of network topology on the dense limit of network spectra remains poorly understood. By considering the configuration model of networks with four distinct degree distributions, we show that the spectral density of the adjacency ma...
The propagation of signalling molecules within cellular networks is affected by network topology, but also by the spatial arrangement of cells in the networks. Understanding the collective reaction--diffusion behaviour in space of signals propagating through cellular networks is an important consideration for example ...
It has recently been shown that interference effects in disordered systems give rise to two non-trivial structures: the coherent backscattering (CBS) peak, a well-known signature of interference effects in the presence of disorder, and the coherent forward scattering (CFS) peak, which emerges when Anderson localization...
We consider the information content h of a scalar multiple-scattered, diffuse wave field $\psi(\vec{r})$ and the information capacity C of a communication channel that employs diffuse waves to transfer the information through a disordered medium. Both h and C are shown to be directly related to the mesoscopic correlat...
We report a molecular dynamics (MD) study of the collective dynamics of a simple monatomic liquid -interacting through a two body potential that mimics that of lithium- across the liquid-glass transition. In the glassy phase we find evidences of a fast relaxation process similar to that recently found in Lennard-Jones...
We consider eigenvectors of the Hamiltonian $H_0$ perturbed by a generic perturbation $V$ modelled by a random matrix from the Gaussian Unitary Ensemble (GUE). Using the supersymmetry approach we derive analytical results for the statistics of the eigenvectors, which are non-perturbative in $V$ and valid for an arbitr...
We report some basic results regarding transport in disordered reaction-diffusion systems with birth (A->2A), death (A->0), and binary competition (2A->A) processes. We consider a model in which the growth process is only allowed to take place in certain areas--"oases"--while the rest of space--the &#...
We investigate the aging dynamics of amorphous SiO2 via molecular dynamics simulations of a quench from a high temperature T_i to a lower temperature T_f. We obtain a microscopic picture of aging dynamics by analyzing single particle trajectories, identifying jump events when a particle escapes the cage formed by its ...
The predictions of the mode-coupling theory (MCT) for the dynamical arrest scenarios in a partly pinned (PP) fluid system are reported. The corresponding dynamical phase diagram is found to be very similar to that of a related quenched-annealed (QA) system.
Hopping charge transport in amorphous semiconductors having spatially correlated exponential density of states has been considered. Average carrier velocity is exactly calculated for the quasi-equilibrium (nondispersive) transport regime.
The $L^2$ localisation landscape of L. Herviou and J. H. Bardarson is a generalisation of the localisation landscape of M. Filoche and S. Mayboroda. We propose a stochastic method to compute the $L^2$ localisation landscape that enables the calculation of landscapes using sparse matrix methods.
We extract the frequency content of a noisy signal by use of Discrete Fourier Transform. Our analysis overcomes the limitations imposed by incommensurate lattices.
We realize experimentally a cold atom system equivalent to the 3D Anderson model of disordered solids where the anisotropy can be controlled by adjusting an experimentally accessible parameter. This allows us to study experimentally the disorder vs anisotropy phase diagram of the Anderson metal-insulator transition.
We consider a classical random-bond Ising model (RBIM) with binary distribution of $\pm K$ bonds on the square lattice at finite temperature. In the phase diagram of this model there is the so-called Nishimori line which intersects the phase boundary at a multicritical point.
We study the statistical properties of the sampled scale-free networks, deeply related to the proper identification of various real-world networks. We exploit three methods of sampling and investigate the topological properties such as degree and betweenness centrality distribution, average path length, assortativity,...
In this paper, we introduce a real-space renormalization transformation for random spin systems on 2D lattices. The general method is formulated for random systems and results from merging two well known real space renormalization techniques, namely the strong disorder renormalization technique (SDRT) and the contract...
We numerically investigate the vibrational spectra of single-component clusters in two-dimensions. Stable configurations of clusters at local energy minima are obtained, and for each the hessian matrix is evaluated and diagonalized to obtain eigenvalues as well as eigenvectors.
Memory effects are ubiquitous in a wide variety of complex physical phenomena, ranging from glassy dynamics and metamaterials to climate models. The Generalised Langevin Equation (GLE) provides a rigorous way to describe memory effects via the so-called memory kernel in an integro-differential equation.
We introduce a Bose-Hubbard Hamiltonian with random disordered interactions as a model to study the interplay of superfluidity and glassiness in a system of three-dimensional hard-core bosons at half-filling. Solving the model using large-scale quantum Monte Carlo simulations, we show that these disordered interaction...
A $d$-dimensional elastic manifold at depinning is described by a renormalized field theory, based on the Functional Renormalization Group (FRG). Here we analyze this theory to 3-loop order, equivalent to third order in $\epsilon=4-d$, where $d$ is the internal dimension.
Glasses possess more low-frequency vibrational modes than predicted by Debye theory. These excess modes are crucial for the understanding the low temperature thermal and mechanical properties of glasses, which differ from those of crystalline solids.
Using a non-thermal local search, called Extremal Optimization (EO), in conjunction with a recently developed scheme for classifying the valley structure of complex systems, we analyze a short-range spin glass. In comparison with earlier studies using a thermal algorithm with detailed balance, we determine which featu...
The random Lorentz gas (RLG) is a minimal model of both percolation and glassiness, which leads to a paradox in the infinite-dimensional, $d\rightarrow\infty$ limit: the localization transition is then expected to be continuous for the former and discontinuous for the latter. As a putative resolution, we have recently...
Systems with two types of agents with a preference for heterophilous interaction produces networks that are more or less close to bipartite. We propose two measures quantifying the notion of bipartivity.
The percolation threshold for flow or conduction through voids surrounding randomly placed spheres is rigorously calculated. With large scale Monte Carlo simulations, we give a rigorous continuum treatment to the geometry of the impenetrable spheres and the spaces between them.
We present a theoretical method for a direct evaluation of the average and reliability error exponents in low-density parity-check error-correcting codes using methods of statistical physics. Results for the binary symmetric channel (BSC) are presented for codes of both finite and infinite connectivity.
We describe the effect of interfaces on classical wave propagation through diffusing layered media. A series resistor model for wave energy transport is introduced and we derive a microscopic expression for the interface resistance.
We study the SUSY-breaking complexity of the Bethe Lattice Spin-Glass in the zero temperature limit. We consider both the Gaussian and the bimodal distribution of the coupling constants.
We investigate the depinning transition in a dirty periodic medium considering a model of layered charge density waves as a prototype system. We find that depinning from strong disorder occurs via a two stage process, where, first, the pinned system experiences a continuous transition into a plastically sliding state ...
We review the theoretical description of the random field Ising and $O(N)$ models obtained from the functional renormalization group, either in its nonperturbative implementation or, in some limits, in perturbative implementations. The approach solves some of the questions concerning the critical behavior of random-fi...
The measured distribution of the single-channel delay time of localized microwave radiation and its correlation with intensity differ sharply from the behavior of diffusive waves. The delay time is found to increase with intensity, while its variance is inversely proportional to the fourth root of the intensity.
We compute the correlation functions of the eigenvalues in the Gaussian unitary ensemble using the fermionic replica method. We show that non--trivial saddle points, which break replica symmetry, must be included in the calculation in order to reproduce correctly the exact results for the correlation functions at larg...
In this review we consider glass states of several disordered systems: vortices in impure superconductors, amorphous magnets, and nematic liquid crystals in random porous media. All these systems can be described by the random-field or random-anisotropy O(N) model.
Distribution of the transmission coefficient T of a long system with a correlated Gaussian disorder is studied analytically and numerically in terms of the generalized Lyapunov exponent (LE) and the cumulants of lnT. The effect of the disorder correlations on these quantities is considered in weak, moderate and strong...
We study rare phase slips due to noise in synchronized Kuramoto oscillator networks. In the small-noise limit, we demonstrate that slips occur via large fluctuations to saddle phase-locked states.
In series of papers Fomin introduced and discussed the so-called robust phases in a system with frozen orientational disorder (with application to superfluid 3He in aerogel). We show that his consideration is based on the erroneous overestimation of the fluctuation energy which comes from the interaction of the Goldst...
Quantum phase transitions of three-dimensional (3D) Weyl semimetals (WSMs) subject to uncorrelated on-site disorder are investigated through quantum conductance calculations and finite-size scaling of localization length. Contrary to previous claims that a direct transition from a WSM to a diffusive metal (DM) occurs,...
We predict the universal power law dependence of localization length on magnetic field in the strongly localized regime. This effect is due to the orbital quantum interference.
We review the close link between intermittent events ('quakes') and extremal noise fluctuations which has been advocated in recent numerical and theoretical work. From the idea that record-breaking noise fluctuations trigger the quakes, an approximate analytical description of non-equilibrium aging as a Poisso...
The subject of this study is the long-time equilibration dynamics of a strongly disordered one-dimensional chain of coupled weakly anharmonic classical oscillators. It is argued that chaos in this system has a very particular spatial structure: it can be viewed as a dilute gas of chaotic spots.
Stark many-body localized (SMBL) systems have been shown both numerically and experimentally to have Bloch many-body oscillations, quantum many-body scars, and fragmentation in the large field tilt limit. Likewise, they are believed to show localization similar to disordered MBL.
We study transport properties of bulk-disordered quasi-one-dimensional (Q1D) wires paying main attention to the role of long-range correlations embedded into the disorder. First, we show that for stratified disorder for which the disorder is the same for all individual chains forming the Q1D wire, the transport proper...
The ordering of the three-dimensional Heisenberg spin glass with the weak random anisotropy in magnetic fields is studied by extensive equilibrium Monte Carlo simulations. Both the spin and the chirality are monitored.
Role of range of interactions in a model of charged particles diffusing on a two-dimensional lattice is studied. We investigate, via Monte Carlo simulations, three models.
The magnetic insulator Gd2Sn2O7 is one of many geometrically frustrated magnetic materials known to exhibit a nonzero muon spin polarization relaxation rate, $\lambda(T)$, down to the lowest temperature (T) studied. Such behaviour is typically interpreted as a significant level of persisting spin dynamics (PSD) of the...
The phase transitions that occur in an infinite-range-interaction Ising ferromagnet in the presence of a double-Gaussian random magnetic field are analyzed. Such random fields are defined as a superposition of two Gaussian distributions, presenting the same width $\sigma$.
We theoretically study the quench dynamics for an isolated Heisenberg spin chain with a random on-site magnetic field, which is one of the paradigmatic models of a many-body localization transition. We use the time-dependent variational principle as applied to matrix product states, which allows us to controllably stu...
The learning properties of finite size polynomial Support Vector Machines are analyzed in the case of realizable classification tasks. The normalization of the high order features acts as a squeezing factor, introducing a strong anisotropy in the patterns distribution in feature space.
We propose a unified framework based on persistent homology (PH) to characterize both local and global structures in disordered systems. It can simultaneously generate local and global descriptors using the same algorithm and data structure, and has shown to be highly effective and interpretable in predicting particle...
Although it is recognized that Anderson localization takes place for all states at a dimension $d$ less or equal $2$, while delocalization is expected for hopping $V(r)$ decreasing with the distance slower or as $r^{-d}$, the localization problem in the crossover regime for the dimension $d=2$ and hopping $V(r) \propto...
We study a minimal model for a relaxor ferroelectric including dipolar interactions, and short-range harmonic and anharmonic forces for the critical modes as in the theory of pure ferroelectrics together with quenched disorder coupled linearly to the critical modes. We present the simplest approximate solution of the ...
We find a renormalized "time-dependent diffusion coefficient", D(t), for pulsed excitation of a nominally diffusive sample by solving the Bethe-Salpeter equation with recurrent scattering. We observe a crossover in dynamics in the transformation from a quasi-1D to a slab geometry implemented by varying the rat...
We theoretically study the conductivity in arrays of metallic grains due to the variable-range multiple cotunneling of electrons with short-range (screened) Coulomb interaction. The system is supposed to be coupled to random stray charges in the dielectric matrix that are only loosely bounded to their spatial position...
The Comment by Ha et al. [<a href="https://arxiv.org/abs/cond-mat/0603787" data-arxiv-id="cond-mat/0603787" class="link-https">cond-mat/0603787</a>] criticizes our recent result [Phys. Rev. Lett. 96, 038701 (2006)] that the contact process (CP) on uncorrelated scale-free (SF) networks does not behave according to hete...
We derive exact expressions for the excess number of clusters b and the excess cumulants b_n of a related quantity at the 2-D percolation point. High-accuracy computer simulations are in accord with our predictions.
We consider an electron system under conditions of strong Anderson localization, taking into account interelectron long-range Coulomb repulsion. We have established that with the electron density going to zero the Coulomb interaction brings the arrangement of the Anderson localized electrons closer and closer to an id...
Percolation theory dictates an intuitive picture depicting correlated regions in complex systems as densely connected clusters. While this picture might be adequate at small scales and apart from criticality, we show that highly correlated sites in complex systems can be inherently disconnected.
In this work we study the condition number of the least square matrix corresponding to scale free networks. We compute a theoretical lower bound of the condition number which proves that they are ill conditioned.
Repeated quantum measurements can generate effective new non-equilibrium dynamics in matter. Here we combine such a measurement driven system with disorder.
The success of deep learning has revealed the application potential of neural networks across the sciences and opened up fundamental theoretical problems. In particular, the fact that learning algorithms based on simple variants of gradient methods are able to find near-optimal minima of highly nonconvex loss function...
Many-body localization (MBL) is a novel prototype of ergodicity breaking due to the emergence of local integrals of motion (LIOMs) in a disordered interacting quantum system. To better understand the role played by the existence of such macroscopically LIOMs, we explore and study some of their structural properties ac...
The recent identification of a time and temperature dependent spin glass correlation length, $\xi({t_w},T)$, has consequences for samples of finite size. Qualitative arguments are given on this basis for departures from t/{t_w} scaling for the time decay of the thermoremanent magnetization, {M_{TRM}}(t,{t_w},T), where...
It is shown that the Bragg glass phase can become unstable with respect to planar defects. A single defect plane that is oriented parallel to the magnetic field as well as to one of the main axis of the Abrikosov flux line lattice is always relevant, whereas we argue that a plane with higher Miller index is irrelevant...
Effects of electron correlations on Anderson insulators have been one of the central themes for recent two decades, suggesting that the Anderson insulating phase turns into a novel insulating state referred to as many body localization (MBL). However, the role of spin degrees of freedom in this dynamical phase transit...
Quantum multicritical points (QMCPs) emerge at the junction of two or more quantum phase transitions due to the interplay of disparate fluctuations, leading to novel universality classes. While quantum critical points have been well characterized, our understanding of QMCPs is much more limited, even though they might...
Motivated by the close relations of the renormalization group with both the holography duality and the deep learning, we propose that the holographic geometry can emerge from deep learning the entanglement feature of a quantum many-body state. We develop a concrete algorithm, call the entanglement feature learning (EF...
Optical measurements of the real and imaginary frequency dependent conductivity of uncompensated n-type silicon are reported. The experiments are done in the quantum limit, $ \hbar\omega > k_{B}T$, across a broad doping range on the insulating side of the Metal-Insulator transition (MIT).
Power-law (PL) time dependent infection growth has been reported in many COVID-19 statistics. In simple SIR models the number of infections grows at the outbreak as $I(t) \propto t^{d-1}$ on $d$-dimensional Euclidean lattices in the endemic phase or follow a slower universal PL at the critical point, until finite size...
Continuing the program begun by the authors in a previous paper, we develop an exact low-density expansion for the random minimum spanning tree (MST) on a finite graph, and use it to develop a continuum perturbation expansion for the MST on critical percolation clusters in space dimension d. The perturbation expansion...
We introduce a Raman profiling method to track homogenization of Ge$_x$Se$_{100-x}$ melts in real time, and show that 2 gram melts reacted at 950°C in high vacuum homogenize in 168 hours on a scale of 10{\mu}m. Homogenization of melts is precursive to self-organization of glasses.
We study the distribution of finite size pseudo-critical points in a one-dimensional random quantum magnet with a quantum phase transition described by an infinite randomness fixed point. Pseudo-critical points are defined in three different ways: the position of the maximum of the average entanglement entropy, the sc...
The structure of flow networks determines their function under normal conditions as well as their response to perturbative damage. Brain vasculature often experiences transient or permanent occlusions in the finest vessels, but it is not clear how these micro-clots affect the large scale blood flow or to what extent t...
We study the statistical and dynamic properties of the systems characterized by an ultrametric space of states and translationary non-invariant symmetric transition matrices of the Parisi type subjected to "locally constant" randomization. Using the explicit expression for eigenvalues of such matrices, we comp...
Tensor renormalization group method (TRG) is a real space renormalization group approach. It has been successfully applied to both classical and quantum systems.
Statistical inference is the science of drawing conclusions about some system from data. In modern signal processing and machine learning, inference is done in very high dimension: very many unknown characteristics about the system have to be deduced from a lot of high-dimensional noisy data.
We investigate the thermodynamic phase transition taking place in the Blume-Capel model in presence of quenched disorder in three dimensions (3D). In particular, performing Exchange Montecarlo simulations, we study the behavior of the order parameters accross the first order phase transition and its related coexistenc...
The analytical solution to the out-of-equilibrium dynamics of mean-field spin glasses has profoundly shaped our understanding of glassy dynamics, which take place in many diverse physical systems. In particular, the idea that during the aging dynamics, the evolution becomes slower and slower, but keeps wandering in an...
We investigate scenarios in which the low-temperature phase of short-range spin glasses comprises thermodynamic states which are nontrivial mixtures of multiple incongruent pure state pairs. We construct a new kind of metastate supported on Gibbs states whose edge overlap values with a reference state fall within a sp...
Using the functional renormalization group (FRG) we study the thermal fluctuations of elastic objects, described by a displacement field u and internal dimension d, pinned by a random potential at low temperature T, as prototypes for glasses. A challenge is how the field theory can describe both typical (minimum energ...
The long-ranged elastic model, which is believed to describe the evolution of a self-affine rough crack-front, is analyzed to linear and non-linear orders. It is shown that the nonlinear terms, while important in changing the front dynamics, are not changing the scaling exponent which characterizes the roughness of th...
The one-dimensional supersymmetric random Hamiltonian $H_{susy}=-\frac{d^2}{dx^2}+\phi^2+\phi'$, where $\phi(x)$ is a Gaussian white noise of zero mean and variance $g$, presents particular spectral and localization properties at low energy: a Dyson singularity in the integrated density of states (IDoS) $N(E)\sim1/...
We numerically investigate the dynamics of entanglement in a chain of spinless fermions with nonrandom but long-range hopping and interactions, and with random on-site energies. For moderate disorder in the absence of interactions, the chain hosts delocalized states at the top of the band which undergo a delocalizatio...
The frustrated Ising model on a two-dimensional lattice with open boundary conditions is revisited. A hidden Z2 gauge symmetry relates models with different frustrations which, however, share the same partition function.
We study the equilibrium properties of the Blume-Emery-Griffiths model with bilinear quenched disorder in the case of attractive as well as repulsive biquadratic interactions. The global phase diagram of the system is calculated in the context of the replica symmetric mean field approximation.
For a system of localised electron states the DC conductivity vanishes at zero temperature, but localised electrons can conduct at finite temperature. Mott gave a theory for the low-temperature conductivity in terms of a variable-range hopping model, which is hard to analyse.

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