Computational Complexity

2012 Edition
| Editors: Robert A. Meyers (Editor-in-Chief)

Field Theoretic Methods

  • Uwe Claus Täuber
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-1800-9_69

Article Outline

Glossary

Definition of the Subject

Introduction

Correlation Functions and Field Theory

Discrete Stochastic Interacting Particle Systems

Stochastic Differential Equations

Future Directions

Acknowledgments

Bibliography

Keywords

Migration 
This is a preview of subscription content, log in to check access

Notes

Acknowledgments

The author would like to acknowledge financial support through the US National Science Foundation grant NSF DMR-0308548. This article is dedicated to the victims of the terrible events at Virginia Tech on April 16, 2007.

Bibliography

  1. 1.
    Lindenberg K, Oshanin G, Tachiya M (eds) (2007) J Phys: Condens Matter 19(6): Special issue containing articles on Chemical kinetics beyond the textbook: fluctuations, many‐particle effects and anomalous dynamics; see: http://www.iop.org/EJ/toc/0953-8984/19/6
  2. 2.
    Alber M, Frey E, Goldstein R (eds) (2007) J Stat Phys 128(1/2): Special issue on Statistical physics in biology; see: http://springerlink.com/content/j4q1ln243968/
  3. 3.
    Murray JD (2002) Mathematical biology, vols. I, II, 3rd edn. Springer, New YorkGoogle Scholar
  4. 4.
    Mobilia M, Georgiev IT, Täuber UC (2007) Phase transitions and spatio‐temporal fluctuations in stochastic lattice Lotka–Volterra models. J Stat Phys 128:447–483. several movies with Monte Carlo simulation animations can be accessed at http://www.phys.vt.edu/~tauber/PredatorPrey/movies/ Google Scholar
  5. 5.
    Washenberger MJ, Mobilia M, Täuber UC (2007) Influence of local carrying capacity restrictions on stochastic predator‐prey models. J Phys: Condens Matter 19:065139, 1–14Google Scholar
  6. 6.
    Ramond P (1981) Field theory – a modern primer. Benjamin/Cummings, ReadingGoogle Scholar
  7. 7.
    Amit DJ (1984) Field theory, the renormalization group, and critical phenomena. World Scientific, SingaporeGoogle Scholar
  8. 8.
    Negele JW, Orland H (1988) Quantum many‐particle systems. Addison-Wesley, Redwood CityMATHGoogle Scholar
  9. 9.
    Parisi G (1988) Statistical field theory. Addison-Wesley, Redwood CityMATHGoogle Scholar
  10. 10.
    Itzykson C, Drouffe JM (1989) Statistical field theory. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  11. 11.
    Le Bellac M (1991) Quantum and statistical field theory. Oxford University Press, OxfordGoogle Scholar
  12. 12.
    Zinn-Justin J (1993) Quantum field theory and critical phenomena. Clarendon Press, OxfordGoogle Scholar
  13. 13.
    Cardy J (1996) Scaling and renormalization in statistical physics. Cambridge University Press, CambridgeGoogle Scholar
  14. 14.
    Janssen HK (1976) On a Lagrangean for classical field dynamics and renormalization group calculations of dynamical critical properties. Z Phys B 23:377–380CrossRefGoogle Scholar
  15. 15.
    De Dominicis C (1976) Techniques de renormalisation de la théorie des champs et dynamique des phénomènes critiques. J Physique (France) Colloq 37:C247–C253Google Scholar
  16. 16.
    Janssen HK (1979) Field-theoretic methods applied to critical dynamics. In: Enz CP (ed) Dynamical critical phenomena and related topics. Lecture Notes in Physics, vol 104. Springer, Heidelberg, pp 26–47Google Scholar
  17. 17.
    Doi M (1976) Second quantization representation for classical many‐particle systems. J Phys A: Math Gen 9:1465–1477CrossRefGoogle Scholar
  18. 18.
    Doi M (1976) Stochastic theory of diffusion‐controlled reactions. J Phys A: Math Gen 9:1479–1495CrossRefGoogle Scholar
  19. 19.
    Grassberger P, Scheunert M (1980) Fock-space methods for identical classical objects. Fortschr Phys 28:547–578MathSciNetCrossRefGoogle Scholar
  20. 20.
    Peliti L (1985) Path integral approach to birth-death processes on a lattice. J Phys (Paris) 46:1469–1482CrossRefGoogle Scholar
  21. 21.
    Peliti L (1986) Renormalisation of fluctuation effects in the \( { A + A \to A } \) reaction. J Phys A: Math Gen 19:L365–L367MathSciNetCrossRefGoogle Scholar
  22. 22.
    Lee BP (1994) Renormalization group calculation for the reaction \( { kA \to \emptyset } \). J Phys A: Math Gen 27:2633–2652CrossRefGoogle Scholar
  23. 23.
    Lee BP, Cardy J (1995) Renormalization group study of the \( { A + B \to \emptyset } \) diffusion‐limited reaction. J Stat Phys 80:971–1007MathSciNetMATHCrossRefGoogle Scholar
  24. 24.
    Mattis DC, Glasser ML (1998) The uses of quantum field theory in diffusion‐limited reactions. Rev Mod Phys 70:979–1002CrossRefGoogle Scholar
  25. 25.
    Täuber UC, Howard MJ, Vollmayr-Lee BP (2005) Applications of field‐theoretic renormalization group methods to reaction‐diffusion problems. J Phys A: Math Gen 38:R79–R131Google Scholar
  26. 26.
    Täuber UC (2007) Field theory approaches to nonequilibrium dynamics. In: Henkel M, Pleimling M, Sanctuary R (eds) Ageing and the glass transition. Lecture Notes in Physics, vol 716. Springer, Berlin, pp 295–348Google Scholar
  27. 27.
    Täuber UC, Critical dynamics: a field theory approach to equilibrium and nonequilibrium scaling behavior. To be published at Cambridge University Press, Cambridge. for completed chapters, see: http://www.phys.vt.edu/~tauber/utaeuber.html
  28. 28.
    Schütz GM (2000) Exactly solvable models for many-body systems far from equilibrium. In: Domb C, Lebowitz JL (eds) Phase transitions and critical phenomena, vol 19. Academic Press, LondonGoogle Scholar
  29. 29.
    Stinchcombe R (2001) Stochastic nonequilibrium systems. Adv Phys 50:431–496CrossRefGoogle Scholar
  30. 30.
    Van Wijland F (2001) Field theory for reaction‐diffusion processes with hard-core particles. Phys Rev E 63:022101, 1–4CrossRefGoogle Scholar
  31. 31.
    Chopard B, Droz M (1998) Cellular automaton modeling of physical systems. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  32. 32.
    Marro L, Dickman R (1999) Nonequilibrium phase transitions in lattice models. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  33. 33.
    Hinrichsen H (2000) Nonequilibrium critical phenomena and phase transitions into absorbing states. Adv Phys 49:815–958CrossRefGoogle Scholar
  34. 34.
    Ódor G (2004) Phase transition universality classes of classical, nonequilibrium systems. Rev Mod Phys 76:663–724Google Scholar
  35. 35.
    Moshe M (1978) Recent developments in Reggeon field theory. Phys Rep 37:255–345MathSciNetCrossRefGoogle Scholar
  36. 36.
    Obukhov SP (1980) The problem of directed percolation. Physica A 101:145–155MathSciNetCrossRefGoogle Scholar
  37. 37.
    Cardy JL, Sugar RL (1980) Directed percolation and Reggeon field theory. J Phys A: Math Gen 13:L423–L427MathSciNetCrossRefGoogle Scholar
  38. 38.
    Janssen HK (1981) On the nonequilibrium phase transition in reaction‐diffusion systems with an absorbing stationary state. Z Phys B 42:151–154CrossRefGoogle Scholar
  39. 39.
    Janssen HK, Täuber UC (2005) The field theory approach to percolation processes. Ann Phys (NY) 315:147–192Google Scholar
  40. 40.
    Grassberger P (1982) On phase transitions in Schlögl's second model. Z Phys B 47:365–374MathSciNetCrossRefGoogle Scholar
  41. 41.
    Janssen HK (2001) Directed percolation with colors and flavors. J Stat Phys 103:801–839MATHCrossRefGoogle Scholar
  42. 42.
    Martin PC, Siggia ED, Rose HA (1973) Statistical dynamics of classical systems. Phys Rev A 8:423–437CrossRefGoogle Scholar
  43. 43.
    Bausch R, Janssen HK, Wagner H (1976) Renormalized field theory of critical dynamics. Z Phys B 24:113–127CrossRefGoogle Scholar
  44. 44.
    Chaikin PM, Lubensky TC (1995) Principles of condensed matter physics. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  45. 45.
    Hohenberg PC, Halperin BI (1977) Theory of dynamic critical phenomena. Rev Mod Phys 49:435–479CrossRefGoogle Scholar
  46. 46.
    Schmittmann B, Zia RKP (1995) Statistical mechanics of driven diffusive systems. In: Domb C, Lebowitz JL (eds) Phase transitions and critical phenomena, vol 17. Academic Press, LondonGoogle Scholar
  47. 47.
    Janssen HK, Schmittmann B (1986) Field theory of long time behaviour in driven diffusive systems. Z Phys B 63:517–520CrossRefGoogle Scholar
  48. 48.
    Leung KT, Cardy JL (1986) Field theory of critical behavior in a driven diffusive system. J Stat Phys 44:567–588MathSciNetCrossRefGoogle Scholar
  49. 49.
    Forster D, Nelson DR, Stephen MJ (1977) Large‐distance and long-time properties of a randomly stirred fluid. Phys Rev A 16:732–749MathSciNetCrossRefGoogle Scholar
  50. 50.
    Kardar M, Parisi G, Zhang YC (1986) Dynamic scaling of growing interfaces. Phys Rev Lett 56:889–892MATHCrossRefGoogle Scholar
  51. 51.
    Barabási AL, Stanley HE (1995) Fractal concepts in surface growth. Cambridge University Press, CambridgeGoogle Scholar
  52. 52.
    Halpin-Healy T, Zhang YC (1995) Kinetic roughening phenomena, stochastic growth, directed polymers and all that. Phys Rep 254:215–414CrossRefGoogle Scholar
  53. 53.
    Krug J (1997) Origins of scale invariance in growth processes. Adv Phys 46:139–282CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Uwe Claus Täuber
    • 1
  1. 1.Department of Physics, Center for Stochastic Processes in Science and EngineeringVirginia Polytechnic Institute and State UniversityBlacksburgUSA