Related papers: Multiscale complexity of two-dimensional Ising sys…
The Griffiths phase in systems with quenched disorder occurs below the ordering transition of the pure system down to the ordering transition of the actual disordered system. While it does not exhibit long-range order, large fluctuations in…
While multiple time scales generally arise in the dynamics of disordered systems, we find multiple time scales in absence of disorder, in a simple model with hard local constraints. The dynamics of the model, which consists of local…
The correlation function of two dimensional Ising model with the nearest neighbours interaction on the finite size lattice with the periodical boundary conditions is derived. The expressions similar to the form factor representation are…
We study Barkhausen noise in a diluted two-dimensional Ising model with the extended domain wall and weak random fields occurring due to coarse graining. We report two types of scaling behavior corresponding to (a) low disorder regime where…
The curvatures of two-particle energy levels with respect to the enclosed magnetic flux in mesoscopic disordered rings are investigated numerically. We find that the typical value of the curvatures is increased by interactions in the…
We study the spatial patterns formed by a system of interacting particles where the mobility of any individual is determined by the population crowding at two different spatial scales. In this way we model the behavior of some biological…
We consider numerically the depinning transition in the random-field Ising model. Our analysis reveals that the three and four dimensional model displays a simple scaling behavior whereas the five dimensional scaling behavior is affected by…
In the spirit of classic works of Wilson on the renormalization group and operator product expansion, a new framework for the study of the theory space of euclidean quantum field theories has been introduced. This formalism is particularly…
The increasing volume of ecologically and biologically relevant data has revealed a wide collection of emergent patterns in living systems. Analyzing different datasets, ranging from metabolic gene-regulatory to species interaction…
We study multifractality in a broad class of disordered systems which includes, e.g., the diluted x-y model. Using renormalized field theory we analyze the scaling behavior of cumulant averaged dynamical variables (in case of the x-y model…
Understanding the functional architecture of complex systems is crucial to illuminate their inner workings and enable effective methods for their prediction and control. Recent advances have introduced tools to characterise emergent…
Creating a quantitative theory for the cortex presents challenges and raises questions. What are the significant scales--micro, meso, or macroscopic? What are the interactions--pairwise, higher order, or mean-field? And what control…
Phase diagram and pattern formation in two-dimensional Ising model with coupling between order parameter and lattice vibrations is investigated by Monte-Carlo simulations. It is shown that if the coupling is strong enough (or phonons are…
We study the dynamics of macroscopic observables such as the magnetization and the energy per degree of freedom in Ising spin models on random graphs of finite connectivity, with random bonds and/or heterogeneous degree distributions. To do…
"Emergence", the phenomenon where a complex system displays properties, behaviours, or dynamics not trivially reducible to its constituent elements, is one of the defining properties of complex systems. Recently, there has been a concerted…
We investigate the dynamics of the quantum Ising model on two-dimensional square lattices up to $16 \times 16$ spins. In the ordered phase, the model is predicted to exhibit dynamically constrained dynamics, leading to confinement of…
Monte Carlo simulations of the short-time dynamic behavior are reported for three-dimensional Ising and XY models with long-range correlated disorder at criticality, in the case corresponding to linear defects. The static and dynamic…
Recent work has shown that probabilistic models based on pairwise interactions-in the simplest case, the Ising model-provide surprisingly accurate descriptions of experiments on real biological networks ranging from neurons to genes.…
Mitochondrial networks exhibit a variety of complex behaviors, including coordinated cell-wide oscillations of energy states as well as a phase transition (depolarization) in response to oxidative stress. Since functional and structural…
Two-dimensional magnetic garnets exhibit complex and fascinating magnetic domain structures, like stripes, labyrinths, cells and mixed states of stripes and cells. These patterns do change in a reversible way when the intensity of an…