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The self-avoiding walk in four dimensions

  • Condensed Matter, Statistical Mechanics
  • Conference paper
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Constructive Physics Results in Field Theory, Statistical Mechanics and Condensed Matter Physics

Part of the book series: Lecture Notes in Physics ((LNP,volume 446))

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Abstract

Recent progress on the self-avoiding walk on a four dimensional hypercubic lattice is presented. Methods for determining the long-time behavior of such walks by studying the Green's function are described.

Lectures given at the Workshop on Constructive Results in Field Theory, Statistical Mechanics and Condensed Matter Physics held at Ecole Polytechnique, Palaiseau France, from July 25–27, 1994.

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References

  1. Brydges, D., Evans, S. N., and Imbrie, J. Z.: Self-Avoiding Walk on a Hierarchical Lattice in Four Dimensions. Ann. Prob. 20, 82–124 (1992)

    Google Scholar 

  2. Brydges, D. and Imbrie, J. Z.: End-to-End Distance for a 4-Dimensional Hierarchical Self-Avoiding Walk. Preprint (1993)

    Google Scholar 

  3. de Gennes, P. G.: Exponents for the excluded volume problem as derived by the Wilson method. Phys. Lett. A 38, 339–340 (1972)

    Google Scholar 

  4. Feldman, J., Magnen, J., Rivasseau, V., and Sénéor, R.: Construction and Borel Summability of Infrared Φ 44 by a Phase Space Expansion. Commun. Math. Phys. 109, 437–480 (1987)

    Article  Google Scholar 

  5. Golowich, S. E., and Imbrie, J. Z.: The Broken Supersymmetry Phase of a Self-Avoiding Random Walk. Commun. Math. Phys., to appear (1994)

    Google Scholar 

  6. Iagolnitzer, D., and Magnen, J.: Polymers in a Weak Random Potential in Dimension Four: Rigorous Renormalization Group Analysis. Commun. Math. Phys., to appear (1994)

    Google Scholar 

  7. Rivasseau, V.: From Perturbative to Constructive Field Theory. Princeton: Princeton University Press (1991)

    Google Scholar 

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Vincent Rivasseau

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© 1995 Springer-Verlag

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Golowich, S.E. (1995). The self-avoiding walk in four dimensions. In: Rivasseau, V. (eds) Constructive Physics Results in Field Theory, Statistical Mechanics and Condensed Matter Physics. Lecture Notes in Physics, vol 446. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59190-7_34

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  • DOI: https://doi.org/10.1007/3-540-59190-7_34

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-59190-0

  • Online ISBN: 978-3-540-49222-1

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