Correlations in the Kosterlitz-Thouless phase of the two-dimensional Coulomb gas |
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Authors: | A. Alastuey F. Cornu |
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Affiliation: | (1) Laboratoire de Physique Théorique et Hautes Energies (laboratoire associé au CNRS), Université de Paris Sud, 91405 Orsay Cedex, France;(2) Present address: Ecole Normale Supérieure de Lyon, Laboratoire de Physique, 46, allée d'Italie, 69364 Lyon Cedex 07, France |
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Abstract: | The particle and charge correlations of the two-dimensional Coulomb gas are studied in the dielectric phase. A term-by-term analysis of the low-fugacity expansions suggests that the large-distance behaviors of the particle correlations are governed by multipolar interactions, similar to what happens in a system of permanent dipoles. These behaviors are compatible with the asymptotic structure of the BGY hierarchy equations; on the other hand, a new identity for the dielectric constant is used to show that the four-particle correlations decay as the dipole-dipole potential 1/r2 when two neutral pairs are separated by a large distancer. Near the zero-density critical point of the Kosterlitz-Thouless transition, we resum the low-fugacity expansions of both 1/ and the charge correlation C(r). We thus retrieve the coupling constant flow equations of the renormalization group as well as the effective interaction energy of the iterated mean-field theory by Kosterlitz and Thouless. The coupling constant at the RG fixed point is then identified with 1/. The nonanalyticity of 1/ at the transition turns out to coincide with the divergence of the low-fugacity series for this quantity. The leading term in the large-distance behavior of C(r) is found to be the same as for external charges. Moreover, we exhibit the subleading terms which also contribute to 1/. |
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Keywords: | Kosterlitz-Thouless transition Coulomb gas dielectric phase correlations fugacity expansions BGY hierarchy |
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