scholarly journals Molecular Stripe Patterns on Surfaces in the Presence of Long-Range Repulsive Electrostatic Interactions: Monte Carlo Simulations and Mean-Field Theory

2021 ◽  
Author(s):  
Christoph Schiel ◽  
Maximilian Vogtland ◽  
Ralf Bechstein ◽  
Angelika Kühnle ◽  
Philipp Maass
Keyword(s):  
Field Theory ◽  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Long Range ◽  
Electrostatic Interactions ◽  
Mean Field Theory ◽  
Mean Field

scholarly journals Effects of homophily and heterophily on preferred-degree networks: mean-field analysis and overwhelming transition

2022 ◽  
Vol 2022 (1) ◽  
pp. 013402
Author(s):  
Xiang Li ◽  
Mauro Mobilia ◽  
Alastair M Rucklidge ◽  
R K P Zia
Keyword(s):  
Field Theory ◽  
Monte Carlo ◽  
Social Interaction ◽  
Monte Carlo Simulations ◽  
Network Structure ◽  
Mean Field Theory ◽  
Mean Field ◽  
Field Analysis ◽  
Long Time

Abstract 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, 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 investigate how the sizes of the communities and the degree of homophily/heterophily affect 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 the larger group, and their mean degree greatly exceeds the preferred degree. This and related phenomena are characterized by 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.

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