Communications in Mathematical Physics

, Volume 137, Issue 2, pp 263–287 | Cite as

A renormalization group analysis of the Kosterlitz-Thouless phase

  • J. Dimock
  • T. R. Hurd


We consider a classical Coulomb gas with a short distance cutoff in two dimensions; equivalently a Sine-Gordon field theory. For low temperature β-1 and low activityz the gas is in a multipole phase, the Kosterlitz-Thouless phase. For β>8π andz sufficiently small we give a complete renormalization group analysis for this phase and show that the flow of the effective measures is toward a free field (infrared asymptotic freedom). This should lead to control over the long distance behavior of the theory.


Renormalization Group Fourier Mode Infinite Volume Renormalization Group Analysis Renormalization Group Transformation 
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  1. [BGN] Benfatto, G., Gallavotti, G., Nicolo, F.: The dipole phase in two-dimensional hierarchical Coulomb gas: Analyticity and correlations decay. Commun. Math. Phys.106, 227–288 (1986)MathSciNetADSGoogle Scholar
  2. [BF] Brydges, D., Federbush, P.: Debye screening. Commun. Math. Phys.73, 197–246 (1980)MathSciNetCrossRefADSGoogle Scholar
  3. [BY] Brydges, D., Yau, H.-T.: Grad Φ perturbations of massless Gaussian fields. Commun. Math. Phys.129, 351–392 (1990)MATHMathSciNetCrossRefADSGoogle Scholar
  4. [D] Dimock, J.: The Kosterlitz-Thouless phase in a hierarchical model. J. Phys.A23, 1207–1215 (1990)MATHMathSciNetCrossRefADSGoogle Scholar
  5. [DH] Dimock, J., Hurd, T. R.: A renormalization group analysis of QED4. preprint (1990)Google Scholar
  6. [FS] Fröhlich, J., Spencer, T.: The Kosterlitz-Thouless transition in two-dimensional Abelian spin systems and the Coulomb gas. Commun. Math. Phys.81, 527–602 (1981)_CrossRefADSGoogle Scholar
  7. [GK] Gawedzki, K., Kupiainen, A.: Block spin renormalization group for dipole gas and ∇Ф)4. Ann. Phys.147, 198–243 (1983), and Lattice dipole gas and ∇Ф)4 models at long distances, decay of correlations and scaling limit. Commun. Math. Phys.92, 531–553 (1984)MathSciNetCrossRefADSGoogle Scholar
  8. [KPW] Kappeler, T., Pinn, K., Wieczerkowski, C.: The renormalization group differential equation and the Kosterlitz-Thouless phase in a hierarchical model, preprint (1990)Google Scholar
  9. [KT] Kosterlitz, J. M., Thouless, D. J.: Ordering, metastability and phase transitions in two-dimensional systems. J. Phys.C6, 1181–1203 (1973)CrossRefADSGoogle Scholar
  10. [MP] Marchetti, D. H. U., Perez, J. F.: A hierarchical model exhibiting the Kosterlitz-Thouless fixed point. Phys. Lett.A118, 74–76 (1986), and The Kosterlitz-Thouless transition in two-dimensional Coulomb gases. J. Stat. Phys.55, 141–156 (1989)MathSciNetCrossRefADSGoogle Scholar
  11. [MKP] Marchetti, D. H. U., Klein, A., Perez, J. F.: Power law fall off in the Kosterlitz-Thouless phase of a two-dimensional lattice Coulomb gas. J. Stat. Phys.60, 137Google Scholar
  12. [Y] Yang, W.-S.: J. Stat. Phys.49, 1–32 (1987)MATHCrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • J. Dimock
    • 1
  • T. R. Hurd
    • 2
  1. 1.Department of MathematicsSUNY at BuffaloBuffaloUSA
  2. 2.Department of MathematicsMcMaster UniversityHamiltonCanada

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