Abstract
We illustrate the mechanism producing the dipole phase in a two dimensional Coulomb system by a detailed analysis of a hierarchical model. We prove the analyticity of the pressure and of the correlations for α2≡βe 2>8π (i.e. right above the usually conjectured value for the Kosterlitz-Thouless phase transition). We find also a power law decay for the correlations with exponent α2/2π as the hierarchical distance goes to infinity.
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Benfatto, G., Cassandro, M., Gallavotti, G., Nicolò, F., Olivieri, O., Presutti, E., Scacciatelli, E.: Some probabilistic techniques in field theory. Commun. Math. Phys.59, 143 (1978)
Benfatto, G., Cassandro, M., Gallavotti, G., Nicolò, F., Olivieri, O., Presutti, E., Scacciatelli, E.: Ultraviolet stability in Euclidean scalar field theories. Commun. Math. Phys.71, 95 (1980)
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);
Nicolò, F.: On the massive sine-Gordon equation in the higher regions of collapse. Commun. Math. Phys.88, 581 (1983)
Fröhlich, J., Spencer, T.: The Kosterlitz-Thouless transition in two dimension Abelian spin systems and the Coulomb gas. Commun. Math. Phys.81, 527 (1981)
Gallavotti, G., Nicolò, F.: The screening phase transitions in the two dimensional Coulomb gas. J. Stat. Phys.39, 133 (1985)
Nicolò, F., Renn, J., Steinmann, A.: The pressure of the two dimensional Coulomb gas at low and intermediate temperatures. Ann. Inst. H. Poincaré (to appear)
Nicolò, F., Renn, J., Steinmann, A.: The sine-Gordon equation in all regions of collapse. Commun. Math. Phys. (in press)
Benfatto, G.: An iterated Mayer expansion for the Yukawa gas. J. Stat. Phys. (to appear)
Speer, E.R.: Mayer coefficients in two dimensional Coulomb systems. J. Stat. Phys. (to appear)
Gallavotti, G.: Renormalization theory and ultraviolet stability for scalar fields via renormalization group methods. Rev. Mod. Phys.57, 471 (1985)
Wilson, K., Kogut, J.: The renormalization group and the ε-expansion. Phys. Rep.12, 75 (1974)
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Communicated by J. Fröhlich
Partially supported by “Ministero della Pubblica Istruzione”, Gruppo Nazionale per la Fisica Matematica del CNR” and Grant A.F.O.S.R.-82-0016C
Partially supported by “Ministero della Pubblica Istruzione” and Grant N.S.F. DMS 85-03333
Partially supported by “Ministera della Pubblica Istruzione”
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Benfatto, G., Gallavotti, G. & Nicolò, F. The dipole phase in the two-dimensional hierarchical Coulomb gas: Analyticity and correlations decay. Commun.Math. Phys. 106, 277–288 (1986). https://doi.org/10.1007/BF01454976
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DOI: https://doi.org/10.1007/BF01454976