Order-disorder phase transition in a cliquey social network
Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, 30059 Kraków, Poland
2 Institute of Theoretical Physics, Cologne University, Zülpicher Str. 77, 50937 Köln, Germany
Revised: 2 May 2007
Published online: 15 June 2007
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
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2007