A phase transition is a change in the nature or number of phases of a system caused by varying external conditions, such as temperature, pressure, composition, or an applied magnetic field. Familiar examples include melting ice and condensing steam, but transitions also occur between states distinguished by magnetic order, electrical properties, or other collective characteristics. They are central to thermodynamics, statistical mechanics, and condensed matter physics. (goldbook.iupac.org)
Phases and equilibrium
A phase is a macroscopically distinct state characterized by its physical properties and organization. The solid, liquid, and gaseous forms of water illustrate ordinary phases, while magnetic and superconducting materials demonstrate that phase distinctions extend beyond these familiar categories. Different phases can consist of the same constituents arranged or correlated differently; changes in collective organization need not involve changes in chemical identity. (damtp.cam.ac.uk)
Under specified constraints, thermodynamic equilibrium is determined by minimizing the appropriate thermodynamic potential. At fixed temperature, pressure, and composition, this is Gibbs free energy. Coexisting phases have equal chemical potentials for each component. A phase diagram represents stable phases and their boundaries as functions of control variables. The liquid–gas coexistence curve terminates at a critical point, beyond which the distinction between liquid and gas disappears. (damtp.cam.ac.uk)
First-order and continuous transitions
A first-order transition has a discontinuity in a first derivative of the equilibrium free energy. Examples include jumps in volume or entropy. Melting and ordinary boiling typically involve latent heat: heat is absorbed or released during conversion between phases without changing the equilibrium transition temperature at fixed pressure. For a coexistence curve,
where , , and are expressed on the same molar or specific basis. This is the Clapeyron equation. (damtp.cam.ac.uk)
In a continuous transition, the order parameter changes continuously, while response functions may become singular. A representative example is the loss of spontaneous magnetization as a ferromagnet is heated through its transition temperature in zero applied field. The historical Ehrenfest classification assigns an order according to the lowest discontinuous free-energy derivative. Modern usage commonly distinguishes first-order from continuous transitions because critical singularities need not fit a simple hierarchy of finite derivative jumps. (damtp.cam.ac.uk)
Order parameters and symmetry
An order parameter quantifies a distinction between phases. Magnetization describes ferromagnetic order, while the density difference between coexisting liquid and gas vanishes at their critical point. Many transitions involve spontaneous symmetry breaking: the governing laws retain a symmetry that the equilibrium state does not. In an idealized magnet, for example, an ordered state selects one of several symmetry-related magnetization directions. (damtp.cam.ac.uk)
Landau theory describes such behavior by expanding a free-energy function in powers of the order parameter, subject to symmetry constraints. Changes in the coefficients alter the positions and number of free-energy minima. The Ising model, consisting of interacting two-valued spins, provides a standard microscopic setting: at temperatures below its critical temperature, reversing the applied field through zero produces a discontinuous reversal of equilibrium magnetization. Heating through the critical temperature at zero field instead produces a continuous transition. (damtp.cam.ac.uk)
Critical phenomena and universality
Near a critical point, fluctuations occur over increasingly large distances. The correlation length characterizes this spatial range and diverges at many continuous transitions in the ideal infinite-system limit. Heat capacity, compressibility, and magnetic susceptibility can display singular behavior described by critical exponents, often through a power law in the distance from the transition. Large density fluctuations can scatter visible light, producing critical opalescence. (damtp.cam.ac.uk)
Universality means that microscopically different systems can share critical exponents and scaling behavior. Their long-distance behavior depends primarily on features such as spatial dimensionality, symmetry, and interaction range. The renormalization group explains this by examining how descriptions change with observation scale. Under ordinary equilibrium assumptions at nonzero temperature, exact singularities emerge in the thermodynamic limit, as system size tends to infinity; finite samples instead show rounded behavior. (damtp.cam.ac.uk)
Transformation kinetics
An equilibrium phase boundary does not by itself determine how quickly transformation occurs. First-order transitions often proceed by nucleation and growth: small regions of the new phase form and subsequently expand. Creating an interface can impose a free-energy barrier, allowing a metastable phase to persist after another phase becomes thermodynamically favored. This distinction between equilibrium stability and transformation rate helps explain delayed phase conversion. (old.goldbook.iupac.org)
Quantum and topological transitions
A quantum phase transition occurs at absolute zero when a nonthermal parameter changes the ground state. Its behavior is governed by quantum mechanics rather than thermal fluctuations. Although experiments operate at nonzero temperatures, nearby quantum critical points can influence measurable finite-temperature properties. (cambridge.org)
Not all transitions are adequately described by conventional symmetry-breaking order parameters. Topological transitions provide important alternatives. In the Berezinskii–Kosterlitz–Thouless transition of suitable two-dimensional systems, bound vortex–antivortex pairs separate as temperature rises. This mechanism differs from ordinary symmetry-breaking transitions and is relevant to thin-film superfluidity and superconductivity. The 2016 Nobel Prize in Physics recognized theoretical discoveries concerning topological phase transitions and topological phases of matter. (nobelprize.org)