Related papers: Ising, Schelling and Self-Organising Segregation
The Schelling model of segregation between two groups of residential agents (Schelling 1971; Schelling 1978) reflects the most abstract view of the non-economic forces of residential migrations: be close to people of 'your own'. The model…
Properties of the two dimensional Ising model with fixed magnetization are deduced from known exact results on the two dimensional Ising model. The existence of a continuous phase transition is shown for arbitrary values of the fixed…
Thomas Schelling proposed an influential simple spatial model to illustrate how, even with relatively mild assumptions on each individual's nearest neighbor preferences, an integrated city would likely unravel to a segregated city, even if…
Spontaneous symmetry breaking occurs in various equilibrium and nonequilibrium systems, where phase transitions are typically marked by a single critical point that separates ordered and disordered regimes. We reveal a novel phenomenon in…
We investigate the Schelling model of social segregation, formulated as an intrinsically non-equilibrium system, in which the agents occupy districts (or patches) rather than sites on a grid. We show that this allows the equations governing…
The Schelling model is a simple agent based model that demonstrates how individuals' relocation decisions generate residential segregation in cities. Agents belong to one of two groups and occupy cells of rectangular space. Agents react to…
A number of novel experimental and theoretical results have recently been obtained on active soft matter, demonstrating the various interesting universal and anomalous features of this kind of driven systems. Here we consider a fundamental…
Over the last few years it was pointed out that certain observables of time-evolving quantum systems may have singularities at certain moments in time, mimicking the singularities physical systems have when undergoing phase transitions.…
The Schelling model is a prototype for agent-based modeling in social systems. We produce a comprehensive analysis of Schelling model rule variants by classifying the space of macroscopic outcomes using phase diagrams. Among 54 rule…
We develop a model in the framework of nuclear fragmentation at thermodynamic equilibrium which can be mapped onto an Ising model with constant magnetization. We work out the thermodynamic properties of the model as well as the properties…
The phase diagram of the dynamic magnetization-reversal transition in pure Ising systems under a pulsed field competing with the existing order can be explained satisfactorily using the classical nucleation theory. Indications of…
We investigate the efficient learning of magnetic phases using artificial neural networks trained on synthetic data, combining computational simplicity with physics-informed strategies. Focusing on the diluted Ising model, which lacks an…
We present a theoretical study of a system with competing short-range ferromagnetic attraction and a long-range anti-ferromagnetic repulsion, in the presence of a uniform external magnetic field. The interplay between these interactions, at…
In this paper we study urban segregation of two different communities A and B, poor and rich, distributed randomly on finite samples, to check cheap and expensive residences. For this purpose we avoid the complications of the Schelling…
In Schelling's segregation model, the successive moves of agents optimizing their own locations lead to a suboptimal segregated distribution of the population, even though all agents have the same preference for mixed neighborhoods. One of…
We investigate the dependence of steady-state properties of Schelling's segregation model on the agents' activation order. Our basic formalism is the Pollicott-Weiss version of Schelling's segregation model. Our main result modifies this…
Schelling segregation is a well-established model used to investigate the dynamics of segregation in agent-based models. Since we consider segregation to be key for the development of political polarisation, we are interested in what…
Behavior of two-time autocorrelation during the phase separation in solid binary mixtures are studied via numerical solutions of the Cahn-Hilliard equation as well as Monte Carlo simulations of the Ising model. Results are analyzed via…
Co-existence of phase segregation and \emph{interconversion} or \emph{isomerization} reaction among molecular species leads to fascinating structure formation in biological and chemical world. Using Monte Carlo simulations of the prototype…
We prove, using the random-cluster model, a strict inequality between site percolation and magnetization in the region of phase transition for the d-dimensional Ising model, thus improving a result of [CNPR76]. We extend this result also at…