Large-Distance Behavior of Particle Correlations in the Two-Dimensional Two-Component Plasma

Abstract

The model under consideration is a two-dimensional two-component plasma, i.e., a continuous system of two species of pointlike particles of opposite charges $\pm 1$, interacting through the logarithmic Coulomb interaction. Using the exact results for the form-factors of an equivalent Euclidean sine-Gordon theory, we derive the large-distance behavior of the pair correlation functions between charged particles. This asymptotic behavior is checked on a few lower orders of its $β$-expansion ($β$ is the inverse temperature) around the Debye-Hückel limit $β\to 0$, and at the free-fermion point $β= 2$ at which the collapse of positive-negative pairs of charges occurs.