A vast variety of systems — from classical thermodynamics to quantum transitions, from plasmas to nuclear, from soft matter to living tissues, from ecosystems to social networks — exhibit abrupt regime changes when a control parameter crosses a critical value.
Common grammar of shifts
Control parameter: temperature, pressure, density, field, stress, flow, error rate, connectivity, noise
Order variable: phase fraction, magnetization, rigidity, global connectivity, coherence, flow rate, viability
Mechanism: symmetry breaking, minima competition, barriers, nucleation, feedbacks, dissipation, topology
Signature: jump, divergence, hysteresis, scaling, absorbing state, topological defects
Universality and critical exponents
Near certain thresholds, observables follow scaling laws characterized by critical exponents. Microscopically different systems can share the same exponents when belonging to the same universality class (Wilson, 1975).
Equilibrium transitions
First-order transitions show discontinuities and latent heat. Continuous transitions show emergent long-range correlations and scaling laws. Dynamic criticality has its own universality classes with critical slowing down.
Out of equilibrium
Out of equilibrium, "phase diagrams" are often stability diagrams delimiting regions of stationary, oscillating, or spatially organized states. Attractor bifurcations, flow-maintained instabilities, and transitions to absorbing states are key patterns.
Applications
Percolation formalizes emergence of global connectivity. Jamming relates density, effective agitation, and stress to blocked states. Active matter shows transitions between disordered and collective ordered motion. Social systems exhibit threshold models of adoption and norm cascades.