2024/10/01 by Jeanne Boursier, Sylvia Serfaty, Boursier, Jeanne +1 · 1 citation
Physics and Astronomy · Engineering · #Dust and Plasma Wave Phenomena #Plasma Diagnostics and Applications #Magnetic confinement fusion research
paper · pdf · doi:10.48550/arxiv.2410.01025
We consider the two-dimensional two-component plasma, or Coulomb gas, consisting of N positive and N negative charges with logarithmic interaction. We introduce a suitable regularization of the interaction by smearing the charges over a small length scale λ, which allows us to give meaning to the system in the continuum at any temperature. We provide an expansion of the free energy in terms of the inverse temperature β, as N → ∞ and λ→ 0. Doing so allows us to show that, for β≥ 2, the charges (for the most part) pair into neutral dipoles of very small size as λ→ 0. This complements the prior work of Leblé, Zeitouni, and the second author, which proved that this does not happen for β< 2, thereby implying a transition at β= 2 from free charges to dipole pairs. Moreover, we obtain an estimate on the size of linear statistics. The description in terms of dipoles is made via a decomposition into nearest-neighbor graphs of the point configurations, à la Gunson-Panta. This is combined with new energy estimates obtained via an electric reformulation of the interaction energy and a ball-growth method, which are expressed in terms of the nearest-neighbor graph distances only. In this way, the model is compared to a reduced nearest-neighbor interaction model, by showing the relative smallness of the dipole-dipole interactions.