Statistical field theory

In <a href="/facts/Theoretical_physics/Cs2Y12rQ">theoretical physics</a>, statistical field theory (SFT) is a theoretical framework that describes <a href="/facts/Phase_transitions/eLP2BY8R">phase transitions</a>. It does not denote a single theory but encompasses many models, including for <a href="/facts/Magnetism/eo75vApl">magnetism</a>, <a href="/facts/Superconductivity/pqQAlSzJ">superconductivity</a>, <a href="/facts/Superfluidity/QuePDujN">superfluidity</a>, <a href="/facts/Topological_phase_transition/EfEnKRSw">topological phase transition</a>, <a href="/facts/Wetting/lGloJUzr">wetting</a> as well as non-equilibrium phase transitions. A SFT is any model in <a href="/facts/Statistical_mechanics/6zMsNYYG">statistical mechanics</a> where the <a href="/facts/Degrees_of_freedom_(physics_and_chemistry)/Rrjl0lnq">degrees of freedom</a> comprise a <a href="/facts/Field_(physics)/FJdAKeRA">field</a> or fields. In other words, the <a href="/facts/Microstate_(statistical_mechanics)/ArXuNn08">microstates</a> of the system are expressed through field configurations. It is closely related to <a href="/facts/Quantum_field_theory/VoewsNJV">quantum field theory</a>, which describes the <a href="/facts/Quantum_mechanics/BRc3Mzgr">quantum mechanics</a> of fields, and shares with it many techniques, such as the <a href="/facts/Path_integral_formulation/6lt2MHkW">path integral formulation</a> and <a href="/facts/Renormalization/B4PdTB4o">renormalization</a>.
If the system involves polymers, it is also known as <a href="/facts/Polymer_field_theory/XtvUHvuW">polymer field theory</a>.
In fact, by performing a <a href="/facts/Wick_rotation/HDU59Ag0">Wick rotation</a> from <a href="/facts/Minkowski_space/vDkfkQJn">Minkowski space</a> to <a href="/facts/Euclidean_space/R2UbzmzM">Euclidean space</a>, many results of statistical field theory can be applied directly to its quantum equivalent. The <a href="/facts/Correlation_function_(quantum_field_theory)/zH7RInAw">correlation functions</a> of a statistical field theory are called <a href="/facts/Schwinger_function/wqVpXznd">Schwinger functions</a>, and their properties are described by the <a href="/facts/Osterwalder%E2%80%93Schrader_axioms/wqVpXznd">Osterwalder–Schrader axioms</a>.
Statistical field theories are widely used to describe systems in <a href="/facts/Polymer_physics/01sWSKtL">polymer physics</a> or <a href="/facts/Biophysics/l9u5gqCy">biophysics</a>, such as <a href="/facts/Polymer/eF32E50K">polymer</a> films, nanostructured block <a href="/facts/Copolymers/35D97DuV">copolymers</a> or <a href="/facts/Polyelectrolyte/3A3jLXkh">polyelectrolytes</a>.

Statistical field theory open-in-new

Statistical field theory