View source for 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]].<ref>{{cite book |last1=Le Bellac |first1=Michel |title=Quantum and Statistical Field Theory |date=1991 |publisher=Clarendon Press |location=Oxford |isbn=978-0198539643}}</ref> It does not denote a single theory but encompasses many models, including for [[magnetism]], [[superconductivity]], [[superfluidity]],<ref>{{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}}</ref> [[topological phase transition]], [[wetting]]<ref>{{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 }}</ref><ref>{{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 }}</ref> as well as non-equilibrium phase transitions.<ref>{{cite book |last1=Täuber |first1=Uwe |title=Critical Dynamics |date=2014 |publisher=Cambridge University Press |location=Cambridge |isbn=978-0-521-84223-5}}</ref> A SFT is any model in [[statistical mechanics]] where the [[Degrees of freedom (physics and chemistry)|degrees of freedom]] comprise a [[Field (physics)|field]] or fields. In other words, the [[Microstate (statistical mechanics)|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 function (quantum field theory)|correlation function]]s of a statistical field theory are called [[Schwinger function]]s, 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]]<ref>{{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}}</ref> or [[polyelectrolyte]]s.<ref>{{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}}</ref>

==Notes==
{{reflist}}

==References==
*{{cite book |title=Statistical Field Theory |volume=I, II |series=Cambridge Monographs on Mathematical Physics |first1=Claude |last1=Itzykson  |first2=Jean-Michel |last2=Drouffe |publisher=Cambridge University Press |date=1991 |isbn=0-521-40806-7}} {{ISBN|0-521-40805-9}}
*{{cite book |first=Giorgio |last=Parisi |title=Statistical Field Theory |url=https://books.google.com/books?id=bivTswEACAAJ |date=1998 |publisher=Perseus Books |isbn=978-0-7382-0051-4 |series=Advanced Book Classics}}
*{{cite book |title=The P(φ)<sub>2</sub> Euclidean (quantum) field theory |first=Barry |last=Simon |publisher=Princeton University Press |date=1974 |isbn=0-691-08144-1}}
*{{cite book |title=Quantum Physics: A Functional Integral Point of View |first1=James |last1=Glimm |first2=Arthur |last2=Jaffe |publisher=Springer |edition=2nd |date=1987 |isbn=0-387-96477-0}}

==External links==
*[https://web.archive.org/web/20060925105340/http://www.gursey.gov.tr/~mgh/rg2006/problemsets.html Problems in Statistical Field Theory]
*[https://web.archive.org/web/20090107204013/http://www-dick.chemie.uni-regensburg.de/group/stephan_baeurle/ Particle and Polymer Field Theory Group]
{{Statistical mechanics topics}}
{{Industrial and applied mathematics}}

[[Category:Applied mathematics]]
[[Category:Mathematical physics]]
[[Category:Statistical field theories| ]]
[[Category:Quantum field theory]]


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