Related papers: Ordering kinetics with long-range interactions: in…
In this paper, we start reviewing the main features of the one-dimensional Ising model with long-range interactions, where the spin-spin coupling decays as a power law, $J(r) \propto r^{-\alpha}$. We then discuss the key properties of the…
We study analytically the ordering kinetics of the two-dimensional long-range voter model on a two-dimensional lattice, where agents on each vertex take the opinion of others at distance $r$ with probability $P(r) \propto r^{-\al}$. The…
The one-dimensional long-range voter model, where an agent takes the opinion of another at distance $r$ with probability $\propto r^{-\alpha}$, is studied analytically. The model displays rich and diverse features as $\alpha$ is changed.…
We investigate the coarsening kinetics in a long-range variant of the Persistent Voter Model in space dimension $d=1$ and 2. In this model agents can hold two confidence levels, normal and zealot. If normal, agents take the opinion of…
We study analytically the ordering kinetics and the final metastable states in the three-dimensional long-range voter model where $N$ agents described by a boolean spin variable $S_i$ can be found in two states (or opinion) $\pm 1$. The…
We investigate the aging properties of the one-dimensional voter model with long-range interactions in its ordering kinetics. In this system, an agent $S_i=\pm 1$ positioned at a lattice vertex $i$, copies the state of another one located…
We study the dynamics of a class of two dimensional stochastic processes, depending on two parameters, which may be interpreted as two different temperatures, respectively associated to interfacial and to bulk noise. Special lines in the…
We study the early time dynamics of bimodal spin systems on $2d$ lattices evolving with different microscopic stochastic updates. We treat the ferromagnetic Ising model with locally conserved order parameter (Kawasaki dynamics), the same…
While the Ising model belongs to the realm of equilibrium statistical mechanics, the voter model is an example of a nonequilibrium system. We examine an opinion formation model, which is a mixture of Ising and voter agents with…
We explore the effect of interplay of interfacial noise and curvature driven dynamics in a binary spin system. An appropriate model is the generalised two dimensional voter model proposed earlier (J. Phys. A: Math. Gen. {\bf 26}, 2317…
The voter model with memory-dependent dynamics is theoretically and numerically studied at the mean-field level. The `internal age', or time an individual spends holding the same state, is added to the set of binary states of the…
Recently, it has been found that an effective long-range interaction is realized among local bistable variables (spins) in systems where the elastic interaction causes ordering of the spins. In such systems, generally we expect both…
In this work, we investigate interactions that simultaneously order a system locally, while keeping it globally disordered. The study is done in the context of the emergence of diversity in opinion propagation models with interactions…
We examine an opinion formation model, which is a mixture of Voter and Ising agents. Numerical simulations show that even a very small fraction ($\sim 1\%$) of the Ising agents drastically changes the behaviour of the Voter model. The Voter…
Consider the voter model on a box of side length $L$ (in the triangular lattice) with boundary votes fixed forever as type 0 or type 1 on two different halves of the boundary. Motivated by analogous questions in percolation, we study…
While the kinetics of domain growth, even for conserved order-parameter dynamics, is widely studied for short-range inter-particle interactions, systems having long-range interactions are receiving attention only recently. Here we present…
An order--disorder phase transition is observed for Ising-like systems even for arbitrarily chosen probabilities of spins flips [K. Malarz et al, Int. J. Mod. Phys. C 22, 719 (2011)]. For such athermal dynamics one must define $(z+1)$ spin…
The voter model is a toy model of consensus formation based on nearest-neighbor interactions. A voter sits at each vertex in a hypercubic lattice (of dimension $d$) and is in one of two possible opinion states. The opinion state of each…
By considering three different spin models belonging to the generalized voter class for ordering dynamics in two dimensions [I. Dornic, \textit{et al.} Phys. Rev. Lett. \textbf{87}, 045701 (2001)], we show that they behave differently from…
We introduce and study a simple model for the dynamics of voting intention in a population of agents that have to choose between two candidates. The level of indecision of a given agent is modeled by its propensity to vote for one of the…