Ordering phase transition in the one-dimensional Axelrod model

Vilone, Daniele; Vespignani, Alessandro; Castellano, Claudio

doi:10.1140/epjb/e2002-00395-2

Cited by 65 publications

(93 citation statements)

References 14 publications

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“…This result holds true for both the two-dimensional [2,4] and the one-dimensional [7,8] versions of Axelrod's model. We recall that the sources of disorder in this model are the stochastic update sequence and the choice of the initial configuration: it is the competition between the disorder of the initial configuration and the ordering bias of the local interactions that is responsible for the nontrivial threshold phenomenon.…”

Section: Introductionmentioning

confidence: 58%

Effect of external fields in Axelrod's model of social dynamics

Peres

Fontanari

2012

Phys. Rev. E

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The study of the effects of spatially uniform fields on the steady-state properties of Axelrod's model has yielded plenty of counterintuitive results. Here, we reexamine the impact of this type of field for a selection of parameters such that the field-free steady state of the model is heterogeneous or multicultural. Analyses of both one-and two-dimensional versions of Axelrod's model indicate that the steady state remains heterogeneous regardless of the value of the field strength. Turning on the field leads to a discontinuous decrease on the number of cultural domains, which we argue is due to the instability of zero-field heterogeneous absorbing configurations. We find, however, that spatially nonuniform fields that implement a consensus rule among the neighborhood of the agents enforce homogenization. Although the overall effects of the fields are essentially the same irrespective of the dimensionality of the model, we argue that the dimensionality has a significant impact on the stability of the field-free homogeneous steady state.

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Section: Introductionmentioning

confidence: 58%

Effect of external fields in Axelrod's model of social dynamics

Peres

Fontanari

2012

Phys. Rev. E

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“…The competition between the disorder of the initial configuration that favors cultural fragmentation and the ordering bias of social influence that favors homogenization results in the nonequilibrium phase transition between those two classes of absorbing states [15]. We note that, similarly to the standard percolation [20], the phase transition occurs in the properties of the absorbing states and so it is static in nature [11].…”

Section: Introductionmentioning

confidence: 76%

“…In the square lattice, the Poisson variant exhibits a continuous phase transition for F = 2 and a discontinuous one for F > 2 [15]. In the onedimensional lattice, only the disordered regime exists for F = 2 and a discontinuous transition between the disordered and the ordered regimes is observed for F > 2 [11].…”

Section: Introductionmentioning

confidence: 99%

“…Here we focus on the case F = 2 only and study the effect of long range interactions on the standard order parameter of Axelrod's model ρ = S max /N that measures the fraction of agents that belong to the largest cultural domain, whose size is denoted by S max , averaged over many independent runs (see, e.g, [11,14,15]). A previous study of the continuous phase transition for F = 2 in the square lattice considered as order parameter the mean density of domains µ = N /N , where N denotes the number of domains of an absorbing configuration, and showed that it vanishes as µ ∼ q − q with β = 0.67±0.01 at the critical point q 0 c = 3.10±0.02 [19].…”

Section: Introductionmentioning

confidence: 99%

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Effect of long-range interactions on the phase transition of Axelrod's model

Reia

Fontanari

2016

Phys. Rev. E

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Axelrod's model with F = 2 cultural features, where each feature can assume k states drawn from a Poisson distribution of parameter q, exhibits a continuous nonequilibrium phase transition in the square lattice. Here we use extensive Monte Carlo simulations and finite size scaling to study the critical behavior of the order parameter ρ, which is the fraction of sites that belong to the largest domain of an absorbing configuration averaged over many runs. We find that it vanishes as ρ ∼ q 0 c − q β with β ≈ 0.25 at the critical point q 0 c ≈ 3.10 and that the exponent that measures the width of the critical region is ν 0 ≈ 2.1. In addition, we find that introduction of long-range links by rewiring the nearest-neighbors links of the square lattice with probability p turns the transition discontinuous, with the critical point q p c increasing from 3.1 to 27.17, approximately, as p increases from 0 to 1. The sharpness of the threshold, as measured by the exponent ν p ≈ 1 for p > 0, increases with the square root of the number of nodes of the resulting small-world network.

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“…The resulting dynamics converges to a global monocultural macroscopic state when initial cultural diversity is below a critical value, while above it homophilic social influence is unable to inforce cultural homogeneity, and multicultural patterns persist asymptotically. This change of behavior has been characterized [5,6,7,8] as a non-equilibrium phase transition. Subsequent studies have analyzed the effects on this transition of different lattice or network structures [9,10], the * Electronic address: mario.floria@gmail.com † Electronic address: yamir.moreno@gmail.com presence of different types of noise ("cultural drift") [11,12], as well as the consideration of external fields (influential media) [13] and global or local non-uniform couplings [14].…”

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confidence: 99%

Residential segregation and cultural dissemination: An Axelrod-Schelling model

et al. 2009

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In the Axelrod's model of cultural dissemination, we consider mobility of cultural agents through the introduction of a density of empty sites and the possibility that agents in a dissimilar neighborhood can move to them if their mean cultural similarity with the neighborhood is below some threshold. While for low values of the density of empty sites the mobility enhances the convergence to a global culture, for high enough values of it the dynamics can lead to the coexistence of disconnected domains of different cultures. In this regime, the increase of initial cultural diversity paradoxically increases the convergence to a dominant culture. Further increase of diversity leads to fragmentation of the dominant culture into domains, forever changing in shape and number, as an effect of the never ending eroding activity of cultural minorities.

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Ordering phase transition in the one-dimensional Axelrod model

Cited by 65 publications

References 14 publications

Effect of external fields in Axelrod's model of social dynamics

Effect of external fields in Axelrod's model of social dynamics

Effect of long-range interactions on the phase transition of Axelrod's model

Residential segregation and cultural dissemination: An Axelrod-Schelling model

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