Abstract
A hierarchical version of two-dimensional lattice Coulomb gases is investigated. Forβ>β c=8π there is a locally stable line of fixed points for the renormalization group (“block charges”) transformations. For\(\beta > \bar \beta _c (\beta _c \leqslant \bar \beta _c \leqslant \tfrac{3}{2}\pi \beta _c )\), these fixed points are globally stable. As a consequence we show that there is no screening of external charges for any activity if\(\beta > \bar \beta _c \). Atβ c a supercritical bifurcation takes place and we investigate the behavior of the model forβ≲β c to show a weak form of screening.
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Marchetti, D.H.U., Fernando Perez, J. The Kosterlitz-Thouless phase transition in two-dimensional hierarchical Coulomb gases. J Stat Phys 55, 141–156 (1989). https://doi.org/10.1007/BF01042594
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DOI: https://doi.org/10.1007/BF01042594