Abstract
We show the existence and asymptotic stability of two fixed points of the renormalization group transformation for the hierarchical two-dimensional Coulomb gas in the sine-Gordon representation and temperatures slightly greater than the critical one. We prove also that the correlations at the fixed points decay as in the hierarchical massive scalar free theory, that is, asd −4xy . We argue that this is the natural definition of screening in the hierarchical approximation.
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References
J. M. Kosterlitz and D. J. Thouless, Ordering, metastability and phase transitions in two-dimensional systems,J. Phys. C 6:1181–1203 (1973).
J. Fröhlich and T. Spencer, The Kosterlitz-Thouless transition in two dimension Abelian spin systems and the Coulomb gas,Commun. Math. Phys. 81:527–602 (1981).
D. H. U. Marchetti, A. Klein, and J. Fernando Ferez, Power law fall off in the Kosterlitz-Thouless phase of a two-dimensional lattice Coulomb gas,J. Stat. Phys. 60:137 (1990).
J. Dimock and T. R. Hurd, A renormalization group analysis of the Kosterlitz-Thouless phase,Commun. Math. Phys. 137:263–287 (1991).
G. Benfatto, G. Gallavotti, and Nicolò, The dipole phase in two dimensional hierarchical Coulomb gas: Analyticity and correlations decay,Commun. Math. Phys. 106:277–288 (1986).
D. H. U. Marchetti and J. Fernando Perez, The Kosterlitz-Thouless phase transition in two-dimensional hierarchical Coulomb gases,J. Stat. Phys. 55:141–156 (1989).
D. Brydges and P. Federbush, Debye screening,Commun. Math. Phys. 73:197–246 (1980).
K. Gawedski and A. Kupiainen, Asymptotic freedom beyond perturbation theory, inLes Houches Summer School (1984).
D. Brydges and T. Kennedy, Mayer expansions and the Hamilton-Jacobi equation,J. Stat. Phys. 48:19–9 (1987).
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Benfatto, G., Renn, J. Nontrivial fixed points and screening in the hierarchical two-dimensional Coulomb gas. J Stat Phys 67, 957–980 (1992). https://doi.org/10.1007/BF01049006
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DOI: https://doi.org/10.1007/BF01049006