Phase diagram of a Schelling segregation model

Gauvin, Laetitia; Vannimenus, J.; Nadal, Jean-Pierre

doi:10.1140/epjb/e2009-00234-0

Cited by 101 publications

(152 citation statements)

References 20 publications

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“…Each time point the lattice has a particular state defined by Equation (6), that produces a r t , which is the set of the homogeneity satisfactions for all the residential members of the lattice. These configurations can be treated as 'microstates' which change according the dynamics of the Schelling model.…”

Section: Discussionmentioning

confidence: 99%

“…The work of [6] develops a method based upon the cluster geometry to measure the label segregation. Approaches to finding a spatial measure which captures obscure cases is an ongoing area of research and can be relied upon for specified classes of patterns [7] produces a physically inspired model for the gradient of the cluster formations so that the arrangements over the iterations resemble that in other physical phenomena but these states are still assess qualitatively by inspection as noted in [8].…”

Section: Introductionmentioning

confidence: 99%

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Examining the Schelling Model Simulation through an Estimation of Its Entropy

Mantzaris

Marich

Halfman

2018

Entropy

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The Schelling model of segregation allows for a general description of residential movements in an environment modeled by a lattice. The key factor is that occupants change positions until they are surrounded by a designated minimum number of similarly labeled residents. An analogy to the Ising model has been made in previous research, primarily due the assumption of state changes being dependent upon the adjacent cell positions. This allows for concepts produced in statistical mechanics to be applied to the Schelling model. Here is presented a methodology to estimate the entropy of the model for different states of the simulation. A Monte Carlo estimate is obtained for the set of macrostates defined as the different aggregate homogeneity satisfaction values across all residents, which allows for the entropy value to be produced for each state. This produces a trace of the estimated entropy value for the states of the lattice configurations to be displayed with each iteration. The results show that the initial random placements of residents have larger entropy values than the final states of the simulation when the overall homogeneity of the residential locality is increased.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Examining the Schelling Model Simulation through an Estimation of Its Entropy

Mantzaris

Marich

Halfman

2018

Entropy

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“…Segregated regions may then appear as agents swap to neighbourhoods whose racial make-up is more to their liking. Subsequently, numerous authors ( [23,6,18,8,7]) have observed the structural similarity between this model and variants of the Ising model considered in statistical mechanics for the analysis of phase-transitions.…”

Section: Introductionmentioning

confidence: 93%

Tipping Points in 1-Dimensional Schelling Models with Switching Agents

2014

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Thomas Schelling's spacial proximity model illustrated how racial segregation can emerge, unwanted, from the actions of citizens acting in accordance with their individual local preferences. One of the earliest agent-based models, it is closely related both to the spin-1 models of statistical physics, and to cascading phenomena on networks. Here a 1-dimensional unperturbed variant of the model is studied, which is open in the sense that agents may enter and exit the model. Following the authors' previous work [1] and that of Brandt, Immorlica, Kamath, and Kleinberg in [4], rigorous asymptotic results are established.This model's openness allows either race to take over almost everywhere. Tipping points are identified between the regions of takeover and staticity. In a significant generalization of the models considered in [1] and [4], the model's parameters comprise the initial proportions of the two races, along with independent values of the tolerance for each race.

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“…However, these approaches are limited to specific utility functions. More recently, physicists have tried to use a statistical physics approach to understand the segregation transition (12)(13)(14). The idea seems promising because statistical physics has successfully bridged the micro-macro gap for physical systems governed by collective dynamics.…”

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confidence: 99%

Competition between collective and individual dynamics

Grauwin

Bertin²,

Lemoy

et al. 2009

Proc. Natl. Acad. Sci. U.S.A.

111

135

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Linking microscopic and macroscopic behavior is at the heart of many natural and social sciences. This apparent similarity conceals essential differences across disciplines: Although physical particles are assumed to optimize the global energy, economic agents maximize their own utility. Here, we solve exactly a Schellinglike segregation model, which interpolates continuously between cooperative and individual dynamics. We show that increasing the degree of cooperativity induces a qualitative transition from a segregated phase of low utility toward a mixed phase of high utility. By introducing a simple function that links the individual and global levels, we pave the way to a rigorous approach of a wide class of systems, where dynamics are governed by individual strategies.socioeconomy | statistical physics | segregation | phase transition | coordination T he intricate relations between the individual and collective levels are at the heart of many natural and social sciences. Different disciplines wonder how atoms combine to form solids (1, 2), neurons give rise to consciousness (3, 4), or individuals shape societies (5, 6). However, scientific fields assume distinct points of view for defining the "normal", or "equilibrium", aggregated state. Physics looks at the collective level, selecting the configurations that minimize the global free energy (2). In contrast, economic agents behave in a selfish way, and equilibrium is attained when no agent can increase its own satisfaction (7). Although similar at first sight, the two approaches lead to radically different outcomes.In this paper, we illustrate the differences between collective and individual dynamics on an exactly solvable model similar to Schelling's segregation model (8). The model considers individual agents that prefer a mixed environment, with dynamics that lead to segregated or mixed patterns at the global level. A "tax" parameter monitors continuously the agents' degree of altruism or cooperativity, i.e., their consideration of the global welfare. At high degrees of cooperativity, the system is in a mixed phase of maximal utility. As the altruism parameter is decreased, a phase transition occurs, leading to segregation. In this phase, the agents' utilities remain low, in spite of continuous efforts to maximize their satisfaction. This paradoxical result of Schelling's segregation model (8) has generated an abundant literature. Many papers have simulated how the global state depends on specific individual utility functions, as reviewed by ref. 9. There have been attempts at solving Schelling's model analytically, in order to provide more general results (10, 11). However, these approaches are limited to specific utility functions. More recently, physicists have tried to use a statistical physics approach to understand the segregation transition (12-14). The idea seems promising because statistical physics has successfully bridged the micro-macro gap for physical systems governed by collective dynamics. However, progress was slowed by lack of an appr...

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Phase diagram of a Schelling segregation model

Cited by 101 publications

References 20 publications

Examining the Schelling Model Simulation through an Estimation of Its Entropy

Examining the Schelling Model Simulation through an Estimation of Its Entropy

Tipping Points in 1-Dimensional Schelling Models with Switching Agents

Competition between collective and individual dynamics

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