Related papers: One-dimensional Ising model built on small-world n…
Small-world networks (SWN), obtained by randomly adding to a regular structure additional links (AL), are of current interest. In this article we explore (based on physical models) a new variant of SWN, in which the probability of realizing…
A dissipative sandpile model (DSM) is constructed and studied on small world networks (SWN). SWNs are generated adding extra links between two arbitrary sites of a two dimensional square lattice with different shortcut densities $\phi$.…
Dynamics of Ising models is a much studied phenomenon and has emerged as a rich field of present-day research. An important dynamical feature commonly studied is the quenching phenomenon below the critical temperature. In this thesis we…
A number of general trends are known to occur in systems displaying secondary processes in glasses and glass formers. Universal features can be identified as components of large and small cooperativeness whose competition leads to excess…
Most real-world networks are endowed with the small-world property, by means of which the maximal distance between any two of their nodes scales logarithmically rather than linearly with their size. The evidence sparkled a wealth of studies…
We show that preferential rewiring, which is supposed to mimick the behaviour of financial agents, changes a directed-network Ising ferromagnet with a single critical point into a model with robust critical behaviour. For the non-rewired…
We consider recent reports on small-world topologies of interaction networks derived from the dynamics of spatially extended systems that are investigated in diverse scientific fields such as neurosciences, geophysics, or meteorology. With…
In this work, we have employed Monte Carlo calculations to study the Ising model on a 2D additive small-world network with long-range interactions depending on the geometric distance between interacting sites. The network is initially…
We introduce a growing one-dimensional quenched spin model that bases on asymmetrical one-side Ising interactions in the presence of external field. Numerical simulations and analytical calculations based on Markov chain theory show that…
We introduce a diffusion model for energetically inhomogeneous systems. A random walker moves on a spin-S Ising configuration, which generates the energy landscape on the lattice through the nearest-neighbors interaction. The underlying…
After a zero temperature quench, we study the kinetics of the one-dimensional Ising model with long-range interactions between spins at distance $r$ decaying as $r^{-\alpha}$, with $\alpha \le 1$. As shown in our recent study [SciPost Phys…
We study the dynamics of the processes in the small-world networks with a power-law degree distribution where every node is considered to be in one of the two available statuses. We present an algorithm for generation of such network and…
We investigate thermodynamic phase transitions of the joint presence of spin glass (SG) and random field (RF) using a random graph model that allows us to deal with the quenched disorder. Therefore, the connectivity becomes a controllable…
The Ising model with ferromagnetic couplings on the Hanoi networks is analyzed with an exact renormalization group. In particular, the fixed-points are determined and the renormalization-group flow for certain initial conditions is…
The antiferromagnetic Ising model in small-world networks generated from two-dimensional regular lattices has been studied. The disorder introduced by long-range connections causes frustration, which gives rise to a spin-glass phase at low…
The zero temperature quenching dynamics of the ferromagnetic Ising model on a densely connected small world network is studied where long range bonds are added randomly with a finite probability $p$. We find that in contrast to the sparsely…
Neural circuits must balance local connectivity constraints against the need for global integration. Here we introduce a minimal wiring rule motivated by synaptic crowding: as a neuron accumulates incoming connections, each additional…
We compare equilibrium probability distributions obtained from Monte Carlo simulations for different spin exchange dynamics with the exact Boltzmann distribution for the fixed magnetization Ising model on small lattices. We present simple…
Network reliability is the probability that a dynamical system composed of discrete elements interacting on a network will be found in a configuration that satisfies a particular property. We introduce a new reliability property, Ising…
We investigate a kinetic Ising model with several single-spin flip dynamics (including Metropolis and heat-bath) on quenched and annealed random regular graphs. As expected, on the quenched structures all proposed algorithms reproduce the…