Communications in Mathematical Physics

, Volume 105, Issue 2, pp 291–326 | Cite as

On the massive sine-Gordon equation in all regions of collapse

  • F. Nicolò
  • J. Renn
  • A. Steinmann


The ultraviolet stability for the cosine interaction in two dimensions and finite volume Λ is rederived for values α2 ∈ [4π, 32/5π[ and proven for the remaining α2 ∈ [4π, 8π[ by using renormalization group methods developed in [G, GN1] to portray renormalized effective potentials arising from a multiscale decomposition.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Renormalization Group 
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  1. [BCGNOPS]
    Benfatto, G., Cassandro, M., Gallavotti, G., Nicolò, F., Olivieri, E., Presutti, E., Scacciatelli, E.: Ultraviolet stability in Euclidean scalar field theories. Commun. Math. Phys.71, 95 (1980)Google Scholar
  2. [BGN]
    Benfatto, G., Gallavotti, G., Nicolò, F.: On the massive Sine-Gordon equation in the first few regions of collapse. Commun. Math. Phys.83, 387 (1982)Google Scholar
  3. [F]
    Fröhlich, J.: Classical and quantum statistical mechanics in one and two dimensions for two-component Yukawa and Coulomb systems. Commun. Math. Phys.47, 233 (1976)Google Scholar
  4. [G]
    Gallavotti, G.: Renormalization theory and ultraviolet stability for scalar fields via renormalization group techniques. Rev. Mod. Phys.57, 471 (1985)Google Scholar
  5. [GN1]
    Gallavotti, G., Nicolò, F.: Renormalization theory in four dimensional scalar field theories (I) and (II). Commun. Math. Phys.100, 545 (1985) and101, 247 (1985)Google Scholar
  6. [GN2]
    Gallavotti, G., Nicolò, F.: The “Screening Phase Transitions” in the two dimensional Coulomb gas. J. Stat. Phys.39, 133 (1985)Google Scholar
  7. [N1]
    Nicolò, F.: On the massive Sine-Gordon equation in the higher regions of collapse. Commun. Math. Phys.88, 681 (1983)Google Scholar
  8. [N2]
    Nicolò, F.: The Coulomb gas systems: Some rigorous results. In: Non-linear equations in classical and quantum field theory. Lecture Notes in Physics, Vol. 226, p. 301. Berlin, Heidelberg, New York: Springer 1985Google Scholar
  9. [NRS]
    Nicolò, F., Renn, J., Steinmann, A.: The pressure of the two dimensional Coulomb gas at low and intermediate temperatures. Preprint, II Università di Roma (1985). To appear on Annales de l'Institut Henri Poincaré, Physique TheoriqueGoogle Scholar
  10. [RS]
    Renn, J., Steinmann, A.: An alternate proof of ultraviolet stability of the two dimensional massive Sine-Gordon field theory in all regions of collapse. Preprint, II Università di Roma (1985)Google Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • F. Nicolò
    • 1
  • J. Renn
    • 2
  • A. Steinmann
    • 3
  1. 1.Dipartimento di MathematicaII Università degli Studi di Roma, Tor VergataRomaItaly
  2. 2.Institut für Theorie der Elementarteilchen (WE4), Fachbereich Physik (FB20)Freie Universität BerlinBerlin 33
  3. 3.Eidgenössische Technische Hochschule, Mathematik, ETH-ZentrumZürichSwitzerland

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