Eur. Phys. J. B 57, 331-335 (2007)
https://doi.org/10.1140/epjb/e2007-00169-4

Order-disorder phase transition in a cliquey social network

¹ 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

Corresponding authors: ^a woloszyn@agh.edu.pl - ^b stauffer@thp.uni-koeln.de - ^c kulakowski@novell.ftj.agh.edu.pl

Received: 23 November 2007
Revised: 2 May 2007
Published online: 15 June 2007

Abstract

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 s_i = ± 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 via weak ties, as discussed by Granovetter in 1973.