The dipole phase in the two-dimensional hierarchical Coulomb gas: Analyticity and correlations decay (Q1104196): Difference between revisions

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 \(\alpha^ 2\equiv \beta e^ 2>8\pi\) (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 \(\alpha^ 2/2\pi\) as the hierarchical distance goes to infinity.