A Spin Glass Model of Social Fragmentation

With the availability of internet and social media the interconnectedness of people has increased tremendously over the past decades. Over the same time span, an increasing level of fragmentation of society into small isolated groups has been observed, which might come with a number of potential catastrophic consequences such as riots, civil wars, governmental shutdowns, and the decline of democracy. If we want to avoid these undesired outcomes, it is necessary to understand the mechanisms leading to social fragmentation.

In a paper(1) inspired by a spin-glass approach towards coalition formation, researchers at the Complexity Science Hub Viena propose a stochastic, coevolutionary model for social fragmentation, closely following social balance theory, where individuals’ opinions and the states of their social links coevolve to minimize the system’s overall stress.

The model that captures five key elements of human societies:

  1. Agency. Humans make their decisions individually.
  2. Social context—social networks. Individuals are constantly influenced by opinions and actions of others in their social neighbourhood, or by other external influences. Humans tend to show homophily.
  3. Stochasticity. Individuals are not fully rational and take random decisions from time to time, that do not maximize utility functions.
  4. Coevolution. Individuals update their opinions as well as their social links. Most of these updates tend to avoid social tension.
  5. Social balance. Social networks show robust structures in positive and negative social links. They exhibit patterns of social balance.
Fig 1. Op. cit. Balance and unbalance realtionships. Red lines represent friendly and cooperative relations, blue lines are negative or hostile links (based on Hieder P-O-X Model

The results deliver a clear and robust message: a society with the ability of a coevolutionary dynamics of opinion and link formation must be expected to have a phase diagram as the one presented in the figure below. A fundamental regime shift (phase transition) happens at critical values.

Fig 3, Op, cit.

The phase diagram shows the existence of a critical connectivity between individuals of a society at a fixed so-called social temperature that characterizes the average volatility of individuals in a society. The higher the social temperature T the more ‘erratic’ or ‘irrational’ is an individual on average. This means that he or she is more likely to update his/her opinion and social ties, regardless if they reduce social stress.

Below the critical connectivity society is in the cohesive phase, where opinions coexist. Above the critical connectivity, society fragments into clusters of individuals who share positive links within the clusters and have negative links between groups. Within the clusters, large patches of uniform opinions form, and a strong reinforcement of homophily is observed. The existence of a critical connectivity is an extremely robust phenomenon; if the connectivity increases above the critical value, society must fragment.

The model also gives an answer to how the fragmented phase can be avoided, and the conclusion is disturbing. There are only two ways out: either to lower the connectivity below the critical density by reducing the number of interaction partners (i.e. social distancing) or, alternatively, to increase the social temperature, meaning that people would update their opinions (and links) randomly more often (behaving in a more irrational way).


(1) Minh Pham, T., Kondor, I., Hanel, R., and Thurner, S. (2020). The effect of social balance on social fragmentation. Journal of The Royal Society Interface 17, 20200752.

Featured Image: Shelby McQuilkin, Social Networking


  1. Interesting. The result is to be expected, as anecdotal evidence shows (e.g. large families find it difficult living together if everybody gives his opinion)
    Of course, as the authors recognise, there are many simplifications that could change the results significantly,

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