Abstract
For a simple, continuum two-dimensional Coulomb gas (with “soft” cutoff), Gallavotti and Nicoló [J. Stat. Phys. 38:133–156 (1985)] have proved the existence of finite coefficients in the Mayer activity expansion up to order 2n below a series of temperature thresholdsT n =T ∞[1+(2n−1)−1] (n=1, 2,...). With this in mind they conjectured that an infinite sequence of intermediate, multipole phases appears between the exponentially screened plasma phase aboveT 1 and the full, unscreened Kosterilitz-Thouless phase belowT ∞≡T KT. We demonstrate that Debye-Hückel-Bjerrum theory, as recently investigated ford=2 dimensions, provides a natural and quite probably correct explanation of the pattern of finite Mayer coefficients while indicating the totalabsence of any intermediate phases at nonzero density ρ; only the KT phase extends to ρ>0.
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Fisher, M.E., Li, Xj. & Levin, Y. On the absence of intermediate phases in the two-dimensional Coulomb gas. J Stat Phys 79, 1–11 (1995). https://doi.org/10.1007/BF02179380
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DOI: https://doi.org/10.1007/BF02179380
Key Words
- Coulomb gas
- sine-Gordon field theory
- two-dimensional Coulomb gases
- Kosterlitz-Thouless phase
- plasma phase
- multipole phases
- Bjerrum ion pairs
- Debye-Hückel theory
- absence of intermediate phases
- Mayer coefficients
- density and virial expansions
- anomalous activity expansions
- equation of state in two dimensions
- restricted primitive model