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

Šamaj, L.

doi:10.1007/s10955-017-1808-9

Cited by 5 publications

(5 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The number of MC-cycles used to reach thermal equilibrium is 10 4 to 1.5 × 10 4 , and thereafter 10 4 to 5 × 10 4 cycles are used to compute thermodynamic averages. The amplitude δL of the trial move is adjusted depending on the coupling parameter Γ in such a way that the acceptance ratio keeps in the (0.30, 0.37) interval 14 .…”

Section: Resultsmentioning

confidence: 99%

“…The current study attempts to model the gapped SE as a 2dTCP with no mixing, or conversely two interacting 2dOCP placed in two electrodes. The 2dOCP has been widely studied [13][14][15][16][17][18][19] because it is a simple system that mimic phase transitions [20][21][22] of real systems as dusty plasmas [23]. One of the peculiarities of these systems is that they form quasi-two-dimensional solids in the strong coupling regime (Γ → ∞).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Monte Carlo simulations of two-component Coulomb gases applied in surface electrodes

Salazar

Bayona-Roa²,

Téllez

2022

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

In this work, we study the gapped Surface Electrode (SE), a planar system composed of two-conductor ﬂat regions at diﬀerent potentials with a gap G between both sheets. The computation of the electric ﬁeld and the surface charge density requires solving Laplace’s equation subjected to Dirichlet conditions (on the electrodes) and Neumann Boundary Conditions over the gap. In this document, the GSE is modeled as a Two-Dimensional Classical Coulomb Gas having punctual charges +q and −q on the inner and outer electrodes, respectively, interacting with an inverse power law 1~r-potential. The coupling parameter Γ between particles inversely depends on temperature and is proportional to q2. Precisely, the density charge arises from the equilibrium states via Monte Carlo (MC) simulations. We focus on the coupling and the gap geometry eﬀect. Mainly on the distribution of particles in the circular and the harmonically-deformed gapped SE. MC simulations diﬀer from electrostatics in the strong coupling regime. The electrostatic approximation and the MC simulations agree in the weak coupling regime where the system behaves as two interacting ionic ﬂuids. That means that temperature is crucial in ﬁnite-size versions of the gapped SE where the density charge cannot be assumed fully continuous as the coupling among particles increases. Numerical comparisons are addressed against analytical descriptions based on an electric vector potential approach, ﬁnding good agreement.

show abstract

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Monte Carlo simulations of two-component Coulomb gases applied in surface electrodes

Salazar

Bayona-Roa²,

Téllez

2022

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

show abstract

“…The aim of this work was to study the effect of charge non-neutrality of a 2D Coulomb system on the finite-size expansion of its grand potential, in particular on the prefactor to the logarithmic term. The previous studies of the symmetric TCP of mobile ±e charges at the collapse point Γ = βe 2 = 2 [13] and of the OCP (jellium) of equivalent mobile e charges in the fixed neutralizing background at the coupling Γ being an even integer [32] were restricted to the disk geometry of the confining domain with the Euler number χ = 1. The previously obtained results suggest that the prefactor to the logarithmic term as a whole does not depend on the charge composition of the Coulomb system.…”

Section: Discussionmentioning

confidence: 99%

“…The case of the non-neutral 2D OCP confined to the disk was studied in Ref. [32]. For any coupling constant being an even integer, the mapping of the system with an excess charge Qe onto an anticommuting field theory formulated on a discrete chain provides for the free energy the large-R expansion of type (1.1), with the coefficient to the logarithmic term B exactly the same as in the relation (1.5).…”

Section: Introductionmentioning

confidence: 99%

Logarithmic Finite-Size Correction in Non-neutral Two-Component Plasma on Sphere

Šamaj

2018

Preprint

Self Cite

View full text Add to dashboard Cite

We consider a general two-component plasma of classical pointlike charges +e (e is say the elementary charge) and −Ze (valency Z = 1, 2, . . .), living on the surface of a sphere of radius R. The system is in thermal equilibrium at the inverse temperature β, in the stability region against collapse of oppositely charged particle pairs βe 2 < 2/Z. We study the effect of the system excess charge Qe on the finite-size expansion of the (dimensionless) grand potential βΩ. By combining the stereographic projection of the sphere onto an infinite plane, the linear response theory and the planar results for the second moments of the species density correlation functions we show that for any βe 2 < 2/Z the large-R expansion of the grand potential is of the form βΩ ∼ A V R 2 + [χ/6 − β(Qe) 2 /2] ln R, where A V is the non-universal coefficient of the volume (bulk) part and the Euler number of the sphere χ = 2. The same formula, containing also a non-universal surface term proportional to R, was obtained previously for the disc domain (χ = 1), in the case of the symmetric (Z = 1) two-component plasma at the collapse point βe 2 = 2 and the jellium model (Z → 0) of identical e-charges in a fixed neutralizing background charge density at any coupling βe 2 being an even integer. Our result thus indicates that the prefactor to the logarithmic finite-size expansion does not depend on the composition of the Coulomb fluid and its non-universal part −β(Qe) 2 /2 is independent of the geometry of the confining domain.

show abstract

“…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%

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

Šamaj

2020

Preprint

Self Cite

View full text Add to dashboard Cite

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.

show abstract

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

Cited by 5 publications

References 41 publications

Monte Carlo simulations of two-component Coulomb gases applied in surface electrodes

Monte Carlo simulations of two-component Coulomb gases applied in surface electrodes

Logarithmic Finite-Size Correction in Non-neutral Two-Component Plasma on Sphere

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

Contact Info

Product

Resources

About