Understanding social fragmentation in a Hamiltonian approach

Like many social phenomena, the formation of individuals` opinions within a society emerges as a result of the complex interactions within friendship-, communication-, or other types of social networks. This happens through a dynamic process in which opinions and the respective network simultaneously co-evolve and influence each other. We currently witness a societal fragmentation where individuals cooperate within groups but become increasingly hostile between groups. While modern social media are often attributed as a cause for this fragmentation, and so called filter bubbles or echo chambers are believed to have a negative impact on opinion formation processes in democracies, its details and dynamics remain largely unknown. We want to clarify the main driving forces behind social fragmentation within the framework of physics-inspired opinion formation models. We propose a model of a toy society that incorporates two fundamentals of social dynamics, opinion formation based on copying opinions of others, and structural social balance, meaning e.g. that my friends friend is my friend. Similar models in physics show phase transitions. They correspond with a rapid change within the system, e.g. the change from ice to water when temperature increases. Similarly to temperature, there are critical parameters that separate a homogenous society from a fragmented one. In this project, we try to find such parameters to better understand, when a society is expected to disintegrate into rivaling groups, impeding democratic decision processes. A main observation is that the increase of communication processes within the population could be involved in the fragmentation process. We want to uncover this possibility within the project.

In today's society, we are witnessing an increasing divide-people form tightly-knit groups where they cooperate internally but grow more hostile toward those outside their circles. This fragmentation emerges from the complex web of social interactions, where opinions and relationships evolve together over time. Two fundamental forces shape these social interactions: homophily and Heider balance. Homophily is the tendency of like-minded individuals to form connections-captured by the saying, "birds of a feather flock together." Heider balance, on the other hand, follows the principle that "the friend of my friend is my friend, and the enemy of my friend is my enemy." These two mechanisms play a crucial role in how opinions spread and how social groups form and evolve. Recently, we have seen a rise in polarization, with people clustering into echo chambers-isolated groups where similar views reinforce one another while differing perspectives are excluded. In this project, we investigated the key forces driving this fragmentation using physics-inspired models of opinion formation. We developed a simplified model of society that incorporates homophily and Heider balance to explore the conditions under which social groups become deeply divided. Just like in physical systems, where matter undergoes phase transitions-such as water turning into ice when temperatures drop-our models reveal that societies can suddenly shift from a state of coexistence to deep polarization. By identifying the key parameters driving these transitions, we gained insight into when and how a society may split into opposing factions. One striking finding is that increased communication-particularly through modern social media-can accelerate fragmentation rather than fostering understanding. The rise of filter bubbles and echo chambers online demonstrates how digital interactions can unintentionally reinforce societal divisions, potentially undermining democratic discourse. By better understanding these mechanisms, we hope to contribute to discussions on how to counteract polarization and build more cohesive societies.