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Order-disorder phase transition in a cliquey social network

M. Woloszyn·D. Stauffer·K. Kulakowski
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Abstract

We investigate the network model of community by Watts, Dodds and Newman (D. J. Watts et al., Science 296 (2002) 1302) as a hierarchy of groups, each of 5 individuals. A homophily parameter $α$ controls the probability proportional to $\exp(-αx)$ of selection of neighbours against distance $x$. The network nodes are endowed with spin-like variables $s_i = \pm 1$, with Ising interaction $J>0$. The Glauber dynamics is used to investigate the order-disorder transition. The transition temperature $T_c$ is close to 3.8 for $α< 0.0$ and it falls down to zero above this value. The result provides a mathematical illustration of the social ability to a collective action {\it via} weak ties, as discussed by Granovetter in 1973.

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M. Woloszyn, D. Stauffer, K. Kulakowski. 2007-04-28. Order-disorder phase transition in a cliquey social network. https://doi.org/10.1140/epjb/e2007-00169-4

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