Order-disorder phase transition in a cliquey social network
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We investigate the network model of community by Watts, Dodds and Newman (D.J. Watts et al., Science 296, 1302 (2002)) 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 si = ± 1, with Ising interaction J > 0. The Glauber dynamics is used to investigate the order-disorder transition. The transition temperature Tc 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 via weak ties, as discussed by Granovetter in 1973.
PACS.89.65.-s Social and economic systems 61.43.-j Disordered solids
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