Abstract
The Mayer series of a Coulomb gas with fixed ultraviolet cutoff is studied in two dimensions. In particular, we show the existence of infinitely many thresholdsT n =(e 2/8πk)(1-1/2n)−1 k=Boltzmann's constant,e=electric charge,n=1, 2,..., which are conjectured to reflect a sequence of transitions from pure multipole phase (the Kosterlitz-Thouless region) to a plasma phase (the Debye screening region) via an infinite number of “intermediate phases.” Mathematically we prove that the Mayer series' coefficients of order up to 2n are finite if the temperatureT is <T n. ForT<T ∞ all the coefficients are finite and the gas can be formally interpreted as a multipole gas with multipoles with finite activity.
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The first author was supported in part by NSF grant No. MCS-8108814 (A03).
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Gallavotti, G., Nicoló, F. The “screening phase transitions” in the two-dimensional Coulomb gas. J Stat Phys 39, 133–156 (1985). https://doi.org/10.1007/BF01007976
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DOI: https://doi.org/10.1007/BF01007976