Year: 1986

Authors: G. Benfatto, G. Gallavotti, F. Nicolo`

Title: The Dipole Phase in the Two-Dimensional Hierarchical Coulomb Gas: Analyticity and Correlations Decay
Communication in Mathematical Physics, 106, 277-288, 1986

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 $\alpha^2=e^2\beta>8\pi$ (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 $\alpja^2/2\pi$ as the hierarchical distance goes to infinity.

Key words:  Quantum fields, Perturbation theory, Renormalization theory, Dipole gas, Sine-Gordon model, $2$-dimensional systems