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We try to design a simple model exhibiting self-organized criticality, which is amenable to a rigorous mathematical analysis. To this end, we modify the generalized Ising Curie-Weiss model by implementing an automatic control of the inverse…
In this paper, we consider a general distributed estimation problem in relay-assisted sensor networks by taking into account time-varying asymmetric communications, fading channels and intermittent measurements. Motivated by centralized…
Infinite projected entangled pair states (iPEPS), the tensor network ansatz for two-dimensional systems in the thermodynamic limit, already provide excellent results on ground-state quantities using either imaginary-time evolution or…
We study the effects of spatially inhomogeneous diffusion on the non-equilibrium phase transition in the contact process. The directed-percolation critical point in the contact process is known to be stable against the addition of a…
This papers presents a generalization of the Weitzman overlapping coefficient, originally defined for two probability density functions, to a setting involving k independent distributions, denoted by Delta. To estimate this generalized…
Infiltration of diffusing particles from one material to another where the diffusion mechanism is either normal or anomalous is a widely observed phenomena. When the diffusion is anomalous we find interesting behaviors: diffusion may lead…
We study in details the dynamics of the one dimensional symmetric trap model, via a real-space renormalization procedure which becomes exact in the limit of zero temperature. In this limit, the diffusion front in each sample consists in two…
This paper extends previous work on echo chambers modeled by an Ising-like system at zero temperature (1. Echo Chambers and random Polarization, Symmetry 2024, 16(12), 1566). There, polarization emerged as a spontaneous symmetry-breaking…
We study domain distributions in the one-dimensional Ising model subject to zero-temperature Glauber and Kawasaki dynamics. The survival probability of a domain, $S(t)\sim t^{-\psi}$, and an unreacted domain, $Q_1(t)\sim t^{-\delta}$, are…
We study the zero temperature random field Ising model as a model for noise and avalanches in hysteretic systems. Tuning the amount of disorder in the system, we find an ordinary critical point with avalanches on all length scales. Using a…
In spin systems such as the Ising model, the local order and disorder can be characterized by the order-parameter and energy density profiles $\langle \sigma ({\bf r}_1) \rangle$ and $\langle \epsilon ({\bf r}_2) \rangle$, respectively.…
From the spread of pollutants in the atmosphere to the transmission of nutrients across cell membranes, anomalous diffusion processes are ubiquitous in natural systems. The ability to understand and control the mechanisms guiding such…
We investigate dimensional reduction, the property that the critical behavior of a system in the presence of quenched disorder in dimension d is the same as that of its pure counterpart in d-2, and its breakdown in the case of the…
We study the influence of disorder on the topological transition from a two-dimensional Dirac semi-metal to an insulating state. This transition is described as a continuous merging of two Dirac points leading to a semi-Dirac spectrum at…
We numerically investigate the necessary ingredients for reentrant behavior in the phase diagram of physical systems. Studies on the possibly simplest model that exhibits reentrance, the two-dimensional random bond Ising model, show that…
Spontaneous symmetry breaking occurs in various equilibrium and nonequilibrium systems, where phase transitions are typically marked by a single critical point that separates ordered and disordered regimes. We reveal a novel phenomenon in…
We consider the disorder-induced correction to the minimal conductance of an anisotropic two-dimensional Dirac node or a three-dimensional Weyl node. An analytical expression is derived for the correction $\delta G$ to the conductance of a…
We consider a semiclassical formulation for the density of states (DOS) of disordered systems in any dimension. We show that this formulation becomes very accurate when the correlation length of the disorder potential is large. The disorder…
Using the tools of random matrix theory we develop a statistical analysis of the transport properties of thermoelectric low-dimensional systems made of two electron reservoirs set at different temperatures and chemical potentials, and…
Tracking tracer particles in heterogeneous environments plays an important role in unraveling the material properties. These heterogeneous structures are often static and depend on the sample realizations. Sample-to-sample fluctuations of…