criticality

Criticality refers to the state of a system at or near a critical point, where small perturbations can trigger disproportionate, qualitative changes in its behavior. The term is used across disciplines, including physics, mathematics, and complex systems theory, to describe threshold conditions, phase transitions, and the emergence of large-scale collective effects.

In physics, criticality is tied to phase transitions. At a critical point, quantities such as correlation length, susceptibility, and fluctuations diverge, and the system exhibits scale invariance and universality. Examples include the liquid–gas critical point and magnetic transitions near the Curie temperature. The study of critical phenomena often employs concepts such as critical exponents and renormalization to describe behavior close to the transition.

In network and complexity theory, self-organized criticality describes systems that naturally evolve toward a critical state where event sizes follow power-law distributions. Prototypical models include sandpile dynamics, earthquakes, and some neural networks. This framework aims to explain how complex systems produce bursts of activity without precise parameter tuning.

In nuclear engineering, criticality denotes a reactor state in which neutron production balances losses, yielding a steady neutron population. The effective multiplication factor k-effective is unity at criticality; k<1 is subcritical and k>1 is supercritical. Accidental or uncontrolled criticality is dangerous and mitigated through safety protocols, design, and operational controls to prevent unintended configurations.

Outside the physical sciences, the concept informs discussions of tipping points and threshold behavior in ecological, economic, and social systems.