Many systems in nature—and in society—can suddenly change their properties: Water freezes at normal pressure at 32°F, a power grid collapses when a central substation fails, or a society splits into opposing factions following a major event. All of these processes are examples of so-called phase transitions—tipping points where a system abruptly shifts into a new state.
“Often, we can predict these transitions easily. We know at what temperature water freezes. But sometimes, it is extremely difficult to foresee when and how these changes will occur,” explains CSH researcher Jan Korbel, one of the authors of the study, which was published in Nature Communications.
Hidden microscopic changes
A particular class of transitions, known as mixed-order transitions, has received little attention so far and is especially difficult to predict.
“In this type of transition, a macroscopic change is triggered by a cascade of microscopic changes that are not easily detectable,” explains author Stefan Thurner from CSH. Once enough small changes accumulate, the system becomes vulnerable to further shifts—and a seemingly insignificant event can suddenly trigger a major transformation.
“Our study shows that these mixed-order abrupt transitions are driven by long-term cascades within the interaction network,” Korbel explains.
“This is very surprising because we have known about these abrupt transitions for more than a hundred years, but their origin remained unknown. We are the first to show that spontaneous microscopic mechanisms within the system drive, as cascades, these abrupt transitions,” adds CSH external faculty member Shlomo Havlin. “And I believe this mechanism explains most—if not all—abrupt transitions that appear in nature, and even in real life.”
“We were able to demonstrate that even when these systems exhibit similar macroscopic behavior, the microscopic details of the transition depend heavily on the precise structure of the system,” says Thurner. As the system approaches the tipping point—also known as the critical point—the time required for the transition to the new phase increases significantly.
To illustrate this: When one is stretching a rubber band, initially, nothing much happens. As it nears its breaking point, however, it may take a long time before it finally snaps—and the exact moment of rupture is difficult to predict.
Wars rarely erupt suddenly
“Unlike the rubber band, what makes mixed-order phase transitions unique is that even when a system surpasses the tipping point, it often takes a long time before the shift to the new phase actually occurs—and there are no reliable indicators of exactly when this will happen,” says Korbel.
Returning to the example of water: In a lake, water molecules primarily influence their immediate neighbors, not molecules on the opposite side of the lake. Under normal conditions, ice crystals form gradually as temperatures drop. However, if lake freezing were a mixed-order phase transition, the water would appear unchanged for a long time—even if the temperature fell below the freezing point. Then, suddenly and unexpectedly, the entire lake would freeze all at once.
“A similar principle applies to social processes. A war may seem to break out suddenly, but it is often preceded by many small, initially inconspicuous developments—political tensions, economic crises, or diplomatic incidents. The underlying networks change. However, the system remains stable for a long time until a seemingly minor event triggers a chain reaction, leading to a sudden transformation,” explains Thurner.
“Research into mixed-order transitions could help us better understand abrupt changes in economics, society, and nature—and perhaps even develop methods to predict such transitions,” says Korbel.
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Models of simple systems
For their analysis, the researchers used theoretical simulations of spin models in real physical systems. In these systems, spins represent tiny magnetic moments that can assume two states.
“The spins typically interact with neighboring particles and tend to align in an energetically favorable configuration,” says Korbel.
In the simulations, the researchers altered the spin of individual particles. If this change lowered the system’s total energy, the new state was likely to persist, as systems generally seek the lowest possible energy state.
“However, if the energy increased, it would theoretically be unfavorable to maintain the new state,” explains Thurner. Yet, fluctuations allow the system to temporarily occupy higher-energy states. Near the tipping point, many competing energy levels emerge, leading to prolonged fluctuations before the system ultimately settles into a stable phase.
Little-studied but highly relevant
Most studies in the field focus on first-order transitions, which occur abruptly but lack long-term microscopic cascades—e.g., water freezing, or second-order transitions, which are not abrupt but gradually—e.g., the loss of magnetization in a ferromagnet.
“What surprised me most about this work is that this type of transition has received so little attention in physics despite its presence in many natural and socio-economic systems and its potential importance for numerous applications,” says Korbel.
At this stage, the research relies solely on simulation data from Monte Carlo simulations.
“Incorporating real-world data could be an extremely exciting avenue for our future research,” says Korbel.
More information:
Jan Korbel et al, Microscopic origin of abrupt mixed-order phase transitions, Nature Communications (2025). DOI: 10.1038/s41467-025-57007-1
Provided by
Complexity Science Hub Vienna
Citation:
When systems suddenly tip: New insights into hard-to-predict transitions (2025, March 24)
