Wigner crystallization and its relation to the poor decay of pair correlations in one-component plasmas of arbitrary dimension

Requardt, Manfred; Wagner, Heinz-Jürgen

doi:10.1007/bf01026570

Cited by 5 publications

(1 citation statement)

References 14 publications

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“…The system is a solid at zero temperature for all s, which has only been proved so far for s 0 and s = −1 (Theorem 35). The Coulomb gas (s = −1) is crystallized at all temperatures275 , whereas translation-invariance is known for s > 1173 and expected for all s 039,381 . Uniqueness is known for s > 2357 and probably expected for all s 0.…”

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Coulomb and Riesz gases: The known and the unknown

Lewin

2022

Preprint

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We review what is known, unknown and expected about the mathematical properties of Coulomb and Riesz gases. Those describe infinite configurations of points in R d interacting with the Riesz potential ±|x| −s (resp. − log |x| for s = 0). Our presentation follows the standard point of view of statistical mechanics, but we also mention how these systems arise in other important situations (e.g. in random matrix theory). The main question addressed in the article is how to properly define the associated infinite point process and characterize it using some (renormalized) equilibrium equation. This is largely open in the long range case s < d. For the convenience of the reader we give the detail of what is known in the short range case s > d. In the last part we discuss phase transitions and mention what is expected on physical grounds.

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confidence: 99%

Coulomb and Riesz gases: The known and the unknown

Lewin

2022

Preprint

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Decay of correlations and related sum rules in a layered classical plasma

Fantoni

Tosi

1995

Il Nuovo Cimento D

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ricevuto il 22 Novembre 1994; approvato il 30 Gennaio 1995)Summary. --The asymptotic behaviours of particle correlation functions and the related sum rules are discussed for a layered classical plasma with e 2/r interactions in the fluid state, in dependence on the number of layers. These properties derive from consistency conditions imposed by screening on the hierarchical equations, as already treated by A. Alastuey and P. A. Martin (J. Stat. Phys., 39, 405 (1985)) for various Coulomb fluids. The main results concern i) the type of clustering of correlations needed for the validity of multipolar sum rules at various orders, ii) the proof that the pair correlation function in a finite multilayer may carry an electric dipole moment and the calculation of its partioning among the layers, and iii) the dimensionality crossover in an infinitely extended or periodically repeated multilayer with varying interlayer spacing and wave vector.PACS 61.20.Gy -Statistical theories of liquid structure.

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Coulomb and Riesz gases: The known and the unknown

Lewin

2022

Journal of Mathematical Physics

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We review what is known, unknown, and expected about the mathematical properties of Coulomb and Riesz gases. Those describe infinite configurations of points in [Formula: see text] interacting with the Riesz potential ±| x|− s (respectively, −log | x| for s = 0). Our presentation follows the standard point of view of statistical mechanics, but we also mention how these systems arise in other important situations (e.g., in random matrix theory). The main question addressed in this Review is how to properly define the associated infinite point process and characterize it using some (renormalized) equilibrium equation. This is largely open in the long range case s < d. For the convenience of the reader, we give the detail of what is known in the short range case s > d. Finally, we discuss phase transitions and mention what is expected on physical grounds.

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Wigner crystallization and its relation to the poor decay of pair correlations in one-component plasmas of arbitrary dimension

Cited by 5 publications

References 14 publications

Coulomb and Riesz gases: The known and the unknown

Coulomb and Riesz gases: The known and the unknown

Decay of correlations and related sum rules in a layered classical plasma

Coulomb and Riesz gases: The known and the unknown

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