Statistical field theory

{{Short description|Framework to describe phase transitions}}

In theoretical physics, statistical field theory (SFT) is a theoretical framework that describes phase transitions.{{cite book |last1=Le Bellac |first1=Michel |title=Quantum and Statistical Field Theory |date=1991 |publisher=Clarendon Press |location=Oxford |isbn=978-0198539643}} It does not denote a single theory but encompasses many models, including for magnetism, superconductivity, superfluidity,{{cite book |last1=Altland |first1=Alexander |last2=Simons |first2=Ben |title=Condensed Matter Field Theory |date=2010 |publisher=Cambridge University Press |location=Cambridge |isbn=978-0-521-76975-4 |edition=2nd}} topological phase transition, wetting{{cite journal |last1=Rejmer |first1=K. |last2=Dietrich |first2=S. |last3=Napiórkowski |first3=M. |title=Filling transition for a wedge |journal=Phys. Rev. E |date=1999 |volume=60 |issue=4 |pages=4027–4042 |doi=10.1103/PhysRevE.60.4027|pmid=11970240 |arxiv=cond-mat/9812115 |bibcode=1999PhRvE..60.4027R |s2cid=23431707 }}{{cite journal |last1=Parry |first1=A.O. |last2=Rascon |first2=C. |last3=Wood |first3=A.J. |title=Universality for 2D Wedge Wetting |journal=Phys. Rev. Lett. |date=1999 |volume=83 |issue=26 |pages=5535–5538 |doi=10.1103/PhysRevLett.83.5535|arxiv=cond-mat/9912388 |bibcode=1999PhRvL..83.5535P |s2cid=119364261 }} as well as non-equilibrium phase transitions.{{cite book |last1=Täuber |first1=Uwe |title=Critical Dynamics |date=2014 |publisher=Cambridge University Press |location=Cambridge |isbn=978-0-521-84223-5}} A SFT is any model in statistical mechanics where the degrees of freedom comprise a field or fields. In other words, the microstates of the system are expressed through field configurations. It is closely related to quantum field theory, which describes the quantum mechanics of fields, and shares with it many techniques, such as the path integral formulation and renormalization.

If the system involves polymers, it is also known as polymer field theory.

In fact, by performing a Wick rotation from Minkowski space to Euclidean space, many results of statistical field theory can be applied directly to its quantum equivalent.{{citation needed|date=November 2018}} The correlation functions of a statistical field theory are called Schwinger functions, and their properties are described by the Osterwalder–Schrader axioms.

Statistical field theories are widely used to describe systems in polymer physics or biophysics, such as polymer films, nanostructured block copolymers{{cite journal |vauthors=Baeurle SA, Usami T, Gusev AA | title= A new multiscale modeling approach for the prediction of mechanical properties of polymer-based nanomaterials | journal=Polymer | year=2006 | volume=47 | pages=8604–8617 | doi=10.1016/j.polymer.2006.10.017 | issue= 26}} or polyelectrolytes.{{cite journal |vauthors=Baeurle SA, Nogovitsin EA | title= Challenging scaling laws of flexible polyelectrolyte solutions with effective renormalization concepts | journal=Polymer | year=2007 | volume=48 | pages=4883–4899 | doi=10.1016/j.polymer.2007.05.080 | issue= 16}}