The existence of negative absolute temperatures in Axelrod’s social influence model

Villegas-Febres, Juan C.; Olivares-Rivas, Wilmer

doi:10.1016/j.physa.2008.02.001

Cited by 12 publications

(9 citation statements)

References 15 publications

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“…In their studies on percolation, Tsang and co-workers [15,18] found that the cluster entropy shows a maximum at the percolation threshold, where a group of neighboring occupied sites forms a cluster that expands from one edge of the 2D lattice to the opposite one causing an abrupt decrease in the cluster entropy of the system. In the context of the Axelrod model, cluster entropy measures the number of cultural groups of different sizes and was first used by Villegas-Febres and Olivares-Rivas [21] in an attempt to establish a connection with thermodynamics. Cluster entropy was also utilized within the Axelrod model to partially characterize the inclusion of repulsion among agents in a regular lattice [9].…”

Section: Introductionmentioning

confidence: 99%

Cluster-size entropy in the Axelrod model of social influence: Small-world networks and mass media

et al. 2011

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We study the Axelrod's cultural adaptation model using the concept of cluster size entropy Sc that gives information on the variability of the cultural cluster size present in the system. Using networks of different topologies, from regular to random, we find that the critical point of the wellknown nonequilibrium monocultural-multicultural (order-disorder) transition of the Axelrod model is unambiguously given by the maximum of the Sc(q) distributions. The width of the cluster entropy distributions can be used to qualitatively determine whether the transition is first-or second-order. By scaling the cluster entropy distributions we were able to obtain a relationship between the critical cultural trait qc and the number F of cultural features in regular networks. We also analyze the effect of the mass media (external field) on social systems within the Axelrod model in a square network. We find a new partially ordered phase whose largest cultural cluster is not aligned with the external field, in contrast with a recent suggestion that this type of phase cannot be formed in regular networks. We draw a new q − B phase diagram for the Axelrod model in regular networks.

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Section: Introductionmentioning

confidence: 99%

Cluster-size entropy in the Axelrod model of social influence: Small-world networks and mass media

et al. 2011

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“…A useful quantity that characterizes a given system is the entropy, which can be de¯ned as: S ¼ Àk B P N m¼1 P m ln P m , where P m is the probability of an agent of belonging to a cluster of m individuals and k B is the Boltzmann constant. 8 This entropy was originally used as function of 1=q, since 1=q represents the probability of adopting a particular value for a feature if q is used as the cultural variability in the original Axelrod model. 8 However, since in this work q represents the mean of a Poisson distribution of values, it already stands for a probability and the entropy is plotted as a function of q.…”

Section: -7mentioning

confidence: 99%

“…8 This entropy was originally used as function of 1=q, since 1=q represents the probability of adopting a particular value for a feature if q is used as the cultural variability in the original Axelrod model. 8 However, since in this work q represents the mean of a Poisson distribution of values, it already stands for a probability and the entropy is plotted as a function of q. Since P ln P ¼ 0 for both P ¼ 0 and P ¼ 1, the entropy adopts values near zero in two cases: (a) when the largest cluster tends to span the whole lattice and (b) when the lattice is completely fragmented.…”

Section: -7mentioning

confidence: 99%

Axelrod Model of Social Influence With Cultural Hybridization

Radillo-Díaz

Pérez

Castillo-Mussot

2012

Int. J. Mod. Phys. C

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Since cultural interactions between a pair of social agents involve changes in both individuals, we present simulations of a new model based on Axelrod's homogenization mechanism that includes hybridization or mixture of the agents' features. In this new hybridization model, once a cultural feature of a pair of agents has been chosen for the interaction, the average of the values for this feature is reassigned as the new value for both agents after interaction. Moreover, a parameter representing social tolerance is implemented in order to quantify whether agents are similar enough to engage in interaction, as well as to determine whether they belong to the same cluster of similar agents after the system has reached the frozen state. The transitions from a homogeneous state to a fragmented one decrease in abruptness as tolerance is increased. Additionally, the entropy associated to the system presents a maximum within the transition, the width of which increases as tolerance does. Moreover, a plateau was found inside the transition for a low-tolerance system of agents with only two cultural features.

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“…Negative temperatures formally exist in paramagnetic materials exposed to external magnetic fields because mathematically the slope (which is proportional to the temperatures) of the entropy as a function of the total energy is negative. Also, the existence of negative temperatures has been studied in social systems in Axelrod's social influence model [13].…”

Section: Introductionmentioning

confidence: 99%