Related papers: Universality in long-range interacting systems: th…
We study the unscreened Coulomb interaction in a one-dimensional electron system at low-energy. We use renormalization group methods and a GW approximation, in order to analyze the model. This yields both a strong wavefunction…
In long-range percolation on $\mathbb{Z}^d$, points $x$ and $y$ are connected by an edge with probability $1-\exp(-\beta\|x-y\|^{-d-\alpha})$, where $\alpha>0$ is fixed and $\beta \geq 0$ is a parameter. As $d$ and $\alpha$ vary, the model…
We use finite size scaling to study Ising spin glasses in two spatial dimensions. The issue of universality is addressed by comparing discrete and continuous probability distributions for the quenched random couplings. The sophisticated…
We rederive the finite size scaling formula for the apparent critical temperature by using Mean Field Theory for the Ising Model above the upper critical dimension. We have also performed numerical simulations in five dimensions and our…
A class of $d$-dimensional reaction-diffusion models interpolating continuously between the diffusion-coagulation and the diffusion-annihilation models is introduced. Exact relations among the observables of different models are…
This article presents an empirical validation of the functional multidimensional scaling model, a novel approach that improves the smoothness of time-varying dissimilarities in a low-dimensional space, embedding a modified Adam stochastic…
Disordered systems submitted to a slowly increasing external stress often reacts with a jerky dynamics characterized by bursts of activity, called avalanches, which are the manifestation of an out-of-equilibrium phase transition. This…
The problem of mapping human close-range proximity networks has been tackled using a variety of technical approaches. Wearable electronic devices, in particular, have proven to be particularly successful in a variety of settings relevant…
Understanding the intriguing physical effects of long-range interactions is a common theme in a host of physical systems. In this work, based on the classical screened Coulomb interacting ring model, we investigate the dynamical effects of…
Dimension reduction lies at the heart of many statistical methods. In regression, dimension reduction has been linked to the notion of sufficiency whereby the relation of the response to a set of predictors is explained by a lower…
The lecture delivered at the \emph{Current Developments in Mathematics} conference (Harvard-MIT, 2021) focused on the recent proof of the Gaussian structure of the scaling limits of the critical Ising and $\varphi^4$ fields in the marginal…
The critical behavior of the Ising model on a fractal lattice, which has the Hausdorff dimension $\log_{4} 12 \approx 1.792$, is investigated using a modified higher-order tensor renormalization group algorithm supplemented with automatic…
Following the pivotal success of learning strategies to win at tasks, solely by interacting with an environment without any supervision, agents have gained the ability to make sequential decisions in complex MDPs. Yet, reinforcement…
We investigate three Ising models on the simple cubic lattice by means of Monte Carlo methods and finite-size scaling. These models are the spin-1/2 Ising model with nearest-neighbor interactions, a spin-1/2 model with nearest-neighbor and…
A spin-$s$ variable-range interacting Ising model may display qualitatively different behaviors depending on the fall-off rate of the interactions, as already seen in equilibrium studies of spin-1/2 systems. We propose a dynamical method…
A method allowing to distinguish interacting from non-interacting systems based on available time series is proposed and investigated. Some facts concerning generalized Renyi dimensions that form the basis of our method are proved. We show…
We consider shock probes in a one-dimensional driven diffusive medium with nearest neighbor Ising interaction (KLS model). Earlier studies based on an approximate mapping of the present system to an effective zero-range process concluded…
A lot of progress has been made recently in our understanding of the random-field Ising model thanks to large-scale numerical simulations. In particular, it has been shown that, contrary to previous statements: the critical exponents for…
Exploiting stochastic path integral theory, we obtain \emph{by simulation} substantial gains in efficiency for the computation of reaction rates in one-dimensional, bistable, overdamped stochastic systems. Using a well-defined measure of…
Many natural systems show emergent phenomena at different scales, leading to scaling regimes with signatures of chaos at large scales and an apparently random behavior at small scales. These features are usually investigated quantitatively…