Statistical field theory

In theoretical physics, statistical field theory (SFT) is a theoretical framework that describes phase transitions.[1] It does not denote a single theory but encompasses many models, including for magnetism, superconductivity, superfluidity[2], topological phase transition, wetting[3][4] as well as non-equilibrium phase transitions[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. 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[6] or polyelectrolytes.[7]

Notes
  1. Le Bellac, Michel (1991). Quantum and Statistical Field Theory. Oxford: Clarendon Press. ISBN 978-0198539643.
  2. Altland, Alexander; Simons, Ben (2010). Condensed Matter Field Theory (2nd ed.). Cambridge: Cambridge University Press. ISBN 978-0-521-76975-4.
  3. Rejmer, K.; Dietrich, S.; Napiórkowski, M. (1999). "Filling transition for a wedge". Phys. Rev. E. 60 (4): 4027--4042. doi:10.1103/PhysRevE.60.4027.
  4. Parry, A.O.; Rascon, C.; Wood, A.J. (1999). "Universality for 2D Wedge Wetting". Phys. Rev. Lett. 83 (26): 5535--5538. doi:10.1103/PhysRevLett.83.5535.
  5. Täuber, Uwe (2014). Critical Dynamics. Cambridge: Cambridge University Press. ISBN 978-0-521-84223-5.
  6. Baeurle SA, Usami T, Gusev AA (2006). "A new multiscale modeling approach for the prediction of mechanical properties of polymer-based nanomaterials". Polymer. 47 (26): 8604–8617. doi:10.1016/j.polymer.2006.10.017.
  7. Baeurle SA, Nogovitsin EA (2007). "Challenging scaling laws of flexible polyelectrolyte solutions with effective renormalization concepts". Polymer. 48 (16): 4883–4899. doi:10.1016/j.polymer.2007.05.080.
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References
  • Statistical Field Theory volumes I and II (Cambridge Monographs on Mathematical Physics) by Claude Itzykson, Jean-Michel Drouffe, Publisher: Cambridge University Press; (March 29, 1991) ISBN 0-521-40806-7 ISBN 0-521-40805-9
  • Statistical field theory by Parisi Giorgio. New York: Perseus Books, 1998.
  • The P(φ)2 Euclidean (quantum) field theory. by Barry Simon. Princeton Univ Press (June 1974) ISBN 0-691-08144-1
  • Quantum Physics: A Functional Integral Point of View by James Glimm, Jaffe. Springer; 2nd edition (May 1987) ISBN 0-387-96477-0
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