Critical phenomena

Critical phenomena are collective behaviors near continuous phase transitions, where fluctuations occur across many scales. They include universal scaling laws and critical exponents shared by otherwise different systems.

Correlation length: A measure of the distance over which fluctuations in a system remain statistically related. It grows near a critical point, allowing fluctuations to span increasingly large distances.
Phase transition: A transformation between distinct macroscopic states of matter as external conditions change. Critical phenomena occur at the continuous boundary between phases.
Liquid–gas critical point: The endpoint of the liquid–gas coexistence curve, above which liquid and gas are indistinguishable. It is the classic experimental setting for critical opalescence and universality.
First-order phase transition: A phase transition involving a discontinuous change in an order parameter and often latent heat. It contrasts with continuous transitions, where critical scaling replaces a jump between phases.
Critical exponent: A number describing how a physical quantity approaches a power-law singularity near a critical point. Exponents quantify the characteristic power laws of critical behavior.
Continuous phase transition: A phase transition at which an order parameter changes continuously and response functions can become singular. This is the transition type whose endpoint supports critical behavior.
Ising model: A lattice model of interacting binary spins used to study magnetism and phase transitions. Its critical behavior provides a tractable model of magnetic ordering.
Mean-field theory: An approximation that replaces interactions with an averaged effective influence from surrounding components. It predicts simple critical exponents but often misses fluctuations in low dimensions.
Universality class: A family of systems sharing the same critical exponents and large-scale behavior. Different microscopic systems can share critical behavior when their symmetries and dimensions match.
Spontaneous symmetry breaking: A state’s loss of a symmetry present in its governing laws, without an explicit symmetry-breaking cause. It often distinguishes the ordered phase from the symmetric phase.

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