Universality of the third-order phase transition in the constrained Coulomb gas

Cunden, Fabio Deelan; Facchi, Paolo; Ligabò, Marilena; Vivo, Pierpaolo

doi:10.1088/1742-5468/aa690c

Cited by 41 publications

(62 citation statements)

References 53 publications

(96 reference statements)

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“…This transition is not of the "pushed-pulled" type like the one at w = 2α, but rather a condensation-type transition as all charges accumulate at the wall for w ≤ −2α. Interestingly, a similar third-order phase transition between the pushed and the pulled phase was recently found [40] by analysing large deviation functions associated with the position of the farthest charge in a d-dimensional jellium model. The limiting distribution of the position of the farthest charge is known in d = 1 (and was computed by Baxter, see Eq.…”

Section: Left Large Deviationsupporting

confidence: 70%

Extreme statistics and index distribution in the classical 1dCoulomb gas

Dhar¹,

Kundu²,

Majumdar³

et al. 2018

J. Phys. A: Math. Theor.

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We consider a one-dimensional gas of N charged particles confined by an external harmonic potential and interacting via the one-dimensional Coulomb potential. For this system we show that in equilibrium the charges settle, on an average, uniformly and symmetrically on a finite region centred around the origin. We study the statistics of the position of the rightmost particle x max and show that the limiting distribution describing its typical fluctuations is different from the Tracy-Widom distribution found in the one-dimensional log-gas. We also compute the large deviation functions which characterise the atypical fluctuations of x max far away from its mean value. In addition, we study the gap between the two rightmost particles as well as the index N + , i.e., the number of particles on the positive semiaxis. We compute the limiting distributions associated to the typical fluctuations of these observables as well as the corresponding large deviation functions. We provide numerical supports to our analytical predictions. Part of these results were announced in a recent Letter, Phys. Rev. Lett. 119, 060601 (2017).

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Section: Left Large Deviationsupporting

confidence: 70%

Extreme statistics and index distribution in the classical 1dCoulomb gas

Dhar¹,

Kundu²,

Majumdar³

et al. 2018

J. Phys. A: Math. Theor.

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“…It would be interesting to explicitly check this, by adding a FI parameter in [25] and doing the corresponding analysis. Finally, it is worth mentioning that at first apparently unrelated works in statistical mechanics, study in fact similar problems and systems [29,30]. and the saddle point equation reduces to the trivial expression f ≡ 0.…”

Section: Discussionmentioning

confidence: 99%

“…The saddle point equation in this case carries only one theta function: 29) and the saddle point is obtained in each phase from this latter expression.…”

Section: Antisymmetric Wilson Loop With One Mass Scalementioning

confidence: 99%

Phase transitions and Wilson loops in antisymmetric representations in Chern–Simons-matter theory

Santilli¹,

Tierz²

2019

J. Phys. A: Math. Theor.

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We study the phase transitions of three-dimensional N = 2 U (N ) Chern-Simons theory on S 3 with a varied number of massive fundamental hypermultiplets and with a Fayet-Iliopoulos parameter. We characterize the various phase diagrams in the decompactification limit, according to the number of different mass scales in the theory. For this, we extend the known solution of the saddle-point equations to the setting where the one cut solution is characterized by asymmetric intervals. We then study the large N limit of Wilson loops in antisymmetric representations, with the additional scaling corresponding to the variation of the size of the representation. We give explicit expressions, both with and without FI terms, and study 1/R corrections for the different phases. These corrections break the perimeter law behavior, as they introduce a scaling with the size of the representation. We show how the phase transitions of the Wilson loops can either be of first or second order and determine the underlying mechanism in terms of the eventual asymmetry of the support of the solution of the saddle-point equation, at the critical points. arXiv:1808.02855v2 [hep-th] 28 Aug 2018 7 Outlook 46 A Free energy second derivatives 47 A.0.1 ζ < m 1 with two mass scales 47 A.0.2 ζ < m 1 with one mass scale 47 A.0.3 ζ > m 1 with two mass scales 48 B Regions with no saddle point 48 B.0.1 Re (z) > 1 or Re (z) < −1 48 B.0.2 Re (z) around ±1

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“…In two dimensions there are difficulties connected with the long-range nature of the − log |x| potential, and we shall not discuss this here." For more background literature on the jellium, see also [3,41,27,1,42,22]. See in particular [51], for the fluctuations of non-neutral jelliums.…”

Section: The Wigner Jellium and Coulomb Gasesmentioning

confidence: 99%

Macroscopic and edge behavior of a planar jellium

Chafäı

García-Zelada

Jung

2020

Journal of Mathematical Physics

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We consider a planar Coulomb gas in which the external potential is generated by a smeared uniform background of opposite-sign charge on a disc. This model can be seen as a two-dimensional Wigner jellium, not necessarily charge neutral, and with particles allowed to exist beyond the support of the smeared charge. The full space integrability condition requires low enough temperature or high enough total smeared charge. This condition does not allow at the same time, total charge neutrality and determinantal structure. The model shares similarities with both the complex Ginibre ensemble and the Forrester-Krishnapur spherical ensemble of random matrix theory. In particular, for a certain regime of temperature and total charge, the equilibrium measure is uniform on a disc as in the Ginibre ensemble, while the modulus of the farthest particle has heavy-tailed fluctuations as in the Forrester-Krishnapur spherical ensemble. We also touch on a higher temperature regime producing a crossover equilibrium measure, as well as a transition to Gumbel edge fluctuations. More results in the same spirit on edge fluctuations are explored by the second author together with Raphael Butez.Contents P →, convergence in law and in probability, respectively, and we annotate X ∼ µ to mean that the law of the random variable X is given by the probability distribution µ. We denote by P(C) the set of probability measures on C, equipped with the topology of weak convergence with respect to continuous and bounded test functions, and its associated Borel σ-field. This topology is metrized by the bounded-Lipschitz metric

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Universality of the third-order phase transition in the constrained Coulomb gas

Cited by 41 publications

References 53 publications

Extreme statistics and index distribution in the classical 1dCoulomb gas

Extreme statistics and index distribution in the classical 1dCoulomb gas

Phase transitions and Wilson loops in antisymmetric representations in Chern–Simons-matter theory

Macroscopic and edge behavior of a planar jellium

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