40 research outputs found
How does homophily shape the topology of a dynamic network?
We consider a dynamic network of individuals that may hold one of two different opinions in a two-party society. As a dynamical model, agents can endlessly create and delete links to satisfy a preferred degree, and the network is shaped by homophily, a form of social interaction. Characterized by the parameter J∈[−1,1], the latter plays a role similar to Ising spins: agents create links to others of the same opinion with probability (1+J)/2, and delete them with probability (1−J)/2. Using Monte Carlo simulations and mean field theory, we focus on the network structure in the steady state. We study the effects of J on degree distributions and the fraction of cross-party links. While the extreme cases of homophily or heterophily (J=±1) are easily understood to result in complete polarization or anti-polarization, intermediate values of J lead to interesting behavior of the network. Our model exhibits the intriguing feature of an "overwhelming transition" occurring when communities of different sizes are subject to sufficient heterophily: agents of the minority group are oversubscribed and their average degree greatly exceeds that of the majority group. In addition, we introduce a novel measure of polarization which displays distinct advantages over the commonly used average edge homogeneity
Metastability in the dilute Ising model
Consider Glauber dynamics for the Ising model on the hypercubic lattice with
a positive magnetic field. Starting from the minus configuration, the system
initially settles into a metastable state with negative magnetization. Slowly
the system relaxes to a stable state with positive magnetization. Schonmann and
Shlosman showed that in the two dimensional case the relaxation time is a
simple function of the energy required to create a critical Wulff droplet.
The dilute Ising model is obtained from the regular Ising model by deleting a
fraction of the edges of the underlying graph. In this paper we show that even
an arbitrarily small dilution can dramatically reduce the relaxation time. This
is because of a catalyst effect---rare regions of high dilution speed up the
transition from minus phase to plus phase.Comment: 49 page
Proceedings of an informal meeting on links between weak and electromagnetic interactions
A correction-to-scaling critical exponent for fluids at order ε3
The critical exponent omega 5, which is a correction to scaling absent in the Ising model, corresponding to insertions of the operator phi 5 in a phi 4 theory near four dimensions, is calculated to third order in 4D.link_to_subscribed_fulltex
Effects of homophily and heterophily on preferred-degree networks: mean-field analysis and overwhelming transition
We investigate the long-time properties of a dynamic, out-of-equilibrium
network of individuals holding one of two opinions in a population consisting
of two communities of different sizes. Here, while the agents' opinions are
fixed, they have a preferred degree which leads them to endlessly create and
delete links. Our evolving network is shaped by homophily/heterophily, which is
a form of social interaction by which individuals tend to establish links with
others having similar/dissimilar opinions. Using Monte Carlo simulations and a
detailed mean-field analysis, we study in detail how the sizes of the
communities and the degree of homophily/heterophily affects the network
structure. In particular, we show that when the network is subject to enough
heterophily, an "overwhelming transition" occurs: individuals of the smaller
community are overwhelmed by links from agents of the larger group, and their
mean degree greatly exceeds the preferred degree. This and related phenomena
are characterized by obtaining the network's total and joint degree
distributions, as well as the fraction of links across both communities and
that of agents having fewer edges than the preferred degree. We use our
mean-field theory to discuss the network's polarization when the group sizes
and level of homophily vary.Comment: 24 pages, 10 figure