Related papers: One-dimensional Ising model built on small-world n…

Recent results from statistical physics show that large classes of complex networks, both man-made and of natural origin, are characterized by high clustering properties yet strikingly short path lengths between pairs of nodes. This class…

Ising machines have attracted attention as efficient solvers for combinatorial optimization problems, which are formulated as ground-state (lowest-energy) search problems of the Ising model. Due to the limited bit-width of coefficients on…

Current world models lack a unified and controlled setting for systematic evaluation, making it difficult to assess whether they truly capture the underlying rules that govern environment dynamics. In this work, we address this open…

The magnetization dynamics of the triangular lattice of Ising spin chains is investigated in the framework of a two-dimensional model. The rigid chains are assumed to interact with the nearest neighboring chains, an external magnetic field,…

We consider in parallel three one-dimensional spin models with kinetic constraints: the paramagnetic constrained Ising chain, the ferromagnetic Ising chain with constrained Glauber dynamics, and the same chain with constrained Kawasaki…

We propose a model for the dynamics of a social system, which includes diffusive effects and a biased rule for spin-flips, reproducing the effect of strategic choices. This model is able to mimic some phenomena taking place during marketing…

Most agent-based models include a social network that describes the structure of interactions within the artificial population. Because of the dramatic impact of this structure on the simulated dynamics, modelers create this network for it…

Binary-state dynamics (such as the susceptible-infected-susceptible (SIS) model of disease spread, or Glauber spin dynamics) on random networks are accurately approximated using master equations. Standard mean-field and pairwise theories…

We propose a simple growing model for the evolution of small-world networks. It is introduced as a modified BA model in which all the edges connected to the new nodes are made locally to the creator and its nearest neighbors. It is found…

Glauber dynamics of the Ising model on a random regular graph is known to mix fast below the tree uniqueness threshold and exponentially slowly above it. We show that Kawasaki dynamics of the canonical ferromagnetic Ising model on a random…

We explore a case example of networks of classical electronic oscillators evolving towards the solution of complex optimization problems. We show that when driven into subharmonic response, a network of such nonlinear electrical resonators…

Rare transitions between long-lived stable states are often analyzed in terms of free energy landscapes computed as functions of a few collective variables. Here, using transitions between geometric phases as example, we demonstrate that…

We propose a new model based on the Ising model with the aim to study synaptic plasticity phenomena in neural networks. It is today well established in biology that the synapses or connections between certain types of neurons are…

A dynamical model of small-world network, with directed links which describe various correlations in social and natural phenomena, is presented. Random responses of every site to the imput message are introduced to simulate real systems.…

It has been suggested that Glauber (inflow) and Sznajd (outflow) zero-temperature dynamics for the one dimensional Ising ferromagnet with the nearest neighbors interactions are equivalent. Here we compare both dynamics from analytical and…

We calculate equilibrium solutions for Ising spin models on `small world' lattices, which are constructed by super-imposing random and sparse Poissonian graphs with finite average connectivity c onto a one-dimensional ring. The nearest…

We study the dynamical response of a two-dimensional Ising model subject to a square-wave oscillating external field. In contrast to earlier studies, the system evolves under a so-called soft Glauber dynamic [P.A. Rikvold and M. Kolesik, J.…

We study an Ising model in a network with disorder induced by the presence of both attractive and repulsive links. This system is subjected to a subthreshold signal, and the goal is to see how the response is enhanced for a given fraction…

We study transition matrices for projected dynamics in the energy-magnetization space, magnetization space and energy space. Several single spin flip dynamics are considered such as the Glauber and Metropolis canonical ensemble dynamics and…

Two new classes of networks are introduced that resemble small-world properties. These networks are recursively constructed but retain a fixed, regular degree. They consist of a one-dimensional lattice backbone overlayed by a hierarchical…