Order-disorder phase transition in a cliquey social network

Woloszyn, M.; Stauffer, D.; Kulakowski, K.

Order-disorder phase transition in a cliquey social network

Authors

Woloszyn, M.

Stauffer, D.

Kulakowski, K.

Description

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.
10 pages, 7 figures