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 thresholds $k T_n =(e^2/8\pi k)(1-1/2n)^{–1}$ 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 temperature $T$ is $< T_n$. For $T<T_\infty$ all the coefficients are finite and the gas can be formally interpreted as a multipole gas with multipoles with finite activity.
The "Screening Phase Transitions" in the Two Dimensional Coulomb Gas / Gallavotti, Giovanni; F., Nicolo`. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - STAMPA. - 39:(1985), pp. 133-156. [10.1007/BF01007976]
The "Screening Phase Transitions" in the Two Dimensional Coulomb Gas
GALLAVOTTI, Giovanni;
1985
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 thresholds $k T_n =(e^2/8\pi k)(1-1/2n)^{–1}$ 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 temperature $T$ is $< T_n$. For $TI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
