Amplitude Function of Asymptotic Correlations Along Charged Wall in Coulomb Fluids

Šamaj, L.

doi:10.1007/s10955-016-1548-2

Cited by 3 publications

(3 citation statements)

References 34 publications

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“…Applying the Möbius conformal transformation to particle coordinates in a disc geometry and going from the disc to an infinite line [81,83], it was found for the present model with counterions only that the function f (1) satisfies the following equations:…”

Section: Transformation Mixing All Anticommuting Componentsmentioning

confidence: 85%

“…There are two basic approaches how to express integer powers of the Vandermonde determinants. The method using a mapping of the 2D Coulomb system onto a 1D lattice anticommuting-field theory was initiated in [72] and subsequently used in a series of works [73,74,75,81,83,84] dealing with sum rules, finite-size corrections, asymptotic decay of two-body correlations along domain's boundaries, etc. Another method using Jack polynomials was developed in [92,93].…”

Section: Introductionmentioning

confidence: 99%

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Attraction of like-charged walls with counterions only: Exact results for the 2D cylinder geometry

Šamaj

2020

Preprint

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We study a 2D system of identical mobile particles on the surface of a cylinder of finite length d and circumference W , immersed in a medium of dielectric constant ε. The two end-circles of the cylinder are like-charged with the fixed uniform charge densities, the particles of opposite charge −e (e being the elementary charge) are coined as "counterions"; the system as a whole is electroneutral. Such a geometry is well defined also for finite numbers of counterions N . Our task is to derive an effective interaction between the end-circles mediated by the counterions in thermal equilibrium at the inverse temperature β. The exact solution of the system at the free-fermion coupling Γ ≡ βe 2 /ε = 2 is used to test the convergence of the pressure as the (even) number of particles increases from N = 2 to ∞. The pressure as a function of distance d is always positive (effective repulsion between the likecharged circles), decaying monotonously; the numerical results for N = 8 counterions are very close to those in the thermodynamic limit N → ∞. For the couplings Γ = 2γ with γ = 1, 2, . . ., there exists a mapping of the continuous two-dimensional (2D) Coulomb system with N particles onto the one-dimensional (1D) lattice model of N sites with interacting sets of anticommuting variables. This allows one to treat exactly the density profile, two-body density and the pressure for the couplings Γ = 4 and 6, up to N = 8 particles. Our main finding is that the pressure becomes negative at large enough distances d if and only if both like-charged walls carry a nonzero charge density. This indicates a like-attraction in the thermodynamic limit N → ∞ as well, starting from a relatively weak coupling constant Γ in between 2 and 4. As a by-product of the formalism, we derive specific sum rules which have direct impact on characteristics of the long-range decay of 2D two-body densities along the two walls.

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Section: Transformation Mixing All Anticommuting Componentsmentioning

confidence: 85%

Section: Introductionmentioning

confidence: 99%

Attraction of like-charged walls with counterions only: Exact results for the 2D cylinder geometry

Šamaj

2020

Preprint

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“…[33] and developed further in Refs. [34,36,37,38,39,40]. The relation between the two methods was established in Ref.…”

Section: Mapping Onto 1d Fermionsmentioning

confidence: 99%

Finite-Size Effects in Non-neutral Two-Dimensional Coulomb Fluids

Šamaj¹

2017

J Stat Phys

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Thermodynamic potential of a neutral two-dimensional (2D) Coulomb fluid, confined to a large domain with a smooth boundary, exhibits at any (inverse) temperature β a logarithmic finite-size correction term whose universal prefactor depends only on the Euler number of the domain and the conformal anomaly number c = −1. A minimal free boson conformal field theory, which is equivalent to the 2D symmetric two-component plasma of elementary ±e charges at coupling constant Γ = βe 2 , was studied in the past. It was shown that creating a non-neutrality by spreading out a charge Qe at infinity modifies the anomaly number to c(Q, Γ ) = −1 + 3Γ Q 2 . Here, we study the effect of non-neutrality on the finite-size expansion of the free energy for another Coulomb fluid, namely the 2D one-component plasma (jellium) composed of identical pointlike e-charges in a homogeneous background surface charge density. For the disk geometry of the confining domain we find that the non-neutrality induces the same change of the anomaly number in the finite-size expansion. We derive this result first at the free-fermion coupling Γ ≡ βe 2 = 2 and then, by using a mapping of the 2D one-component plasma onto an anticommuting field theory formulated on a chain, for an arbitrary coupling constant.

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Attraction of Like-Charged Walls with Counterions Only: Exact Results for the 2D Cylinder Geometry

Šamaj

2020

J Stat Phys

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Amplitude Function of Asymptotic Correlations Along Charged Wall in Coulomb Fluids

Cited by 3 publications

References 34 publications

Attraction of like-charged walls with counterions only: Exact results for the 2D cylinder geometry

Attraction of like-charged walls with counterions only: Exact results for the 2D cylinder geometry

Finite-Size Effects in Non-neutral Two-Dimensional Coulomb Fluids

Attraction of Like-Charged Walls with Counterions Only: Exact Results for the 2D Cylinder Geometry

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