Phase Transitions and Critical Phenomena
Phase transitions are abrupt changes in the state of matter, and near continuous transitions diverse systems share universal critical behavior captured by scaling and the renormalization group.
Definition
A phase transition is a qualitative change in the macroscopic state of a system as a control parameter is varied, and critical phenomena are the universal singular behaviors of thermodynamic quantities near continuous transitions, organized by symmetry and dimensionality rather than microscopic detail.
Scope
This area covers the classification of phase transitions into first-order and continuous types, lattice models such as the Ising model and their exact and approximate solutions, Landau's theory of order parameters and symmetry breaking, the singular behavior near critical points described by critical exponents, the scaling hypothesis, and the renormalization group that explains universality. The microscopic statistics underlying these models come from the ensembles and quantum-statistics areas.
Sub-topics
Core questions
- How are first-order and continuous phase transitions distinguished thermodynamically?
- Why do thermodynamic quantities diverge with universal exponents near a critical point?
- How does an order parameter encode spontaneous symmetry breaking?
- Why does the renormalization group explain the universality of critical behavior?
Key concepts
- First-order versus continuous transitions
- Order parameter and spontaneous symmetry breaking
- Critical exponents and universality classes
- Scaling hypothesis
- Renormalization group
Key theories
- Landau theory of phase transitions
- A continuous transition is described by expanding the free energy in powers of an order parameter respecting the system's symmetry; minimizing it predicts symmetry breaking and the mean-field critical exponents.
- Renormalization group and universality
- Successively coarse-graining a system defines a flow in the space of couplings whose fixed points govern critical behavior, explaining why systems differing microscopically share the same critical exponents.
Clinical relevance
The theory of phase transitions describes melting, boiling, magnetism, superconductivity, and superfluidity, and its renormalization-group methods extend to polymers, percolation, turbulence, and even analogies in cosmology and quantum field theory.
History
From van der Waals's continuous account of liquid-gas coexistence and Landau's 1937 order-parameter theory, the field advanced through Onsager's 1944 exact solution of the two-dimensional Ising model and culminated in Wilson's renormalization group of the early 1970s, which explained universality.
Key figures
- Lev Landau
- Lars Onsager
- Leo Kadanoff
- Kenneth Wilson
Related topics
Seminal works
- wilson1971
- landaulifshitz1980stat
- goldenfeld1992
Frequently asked questions
- What is universality in critical phenomena?
- It is the observation that the critical exponents and scaling functions near a continuous transition depend only on a few features -- the spatial dimension, the symmetry of the order parameter, and the range of interactions -- and not on microscopic details, so very different systems fall into the same universality class.
- What distinguishes a first-order from a continuous transition?
- A first-order transition involves a latent heat and a discontinuous jump in the order parameter, as in boiling water, whereas a continuous transition has the order parameter vary smoothly to zero with diverging fluctuations and no latent heat.