States of one-dimensional Coulomb systems as simple examples of ? vacua and confinement

Aizenman, Michael; Fröhlich, Jürg

doi:10.1007/bf01013176

Cited by 12 publications

(8 citation statements)

References 22 publications

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“…where the initial and final points of the process X n are fixed at zero. This representation is essentially a 1D Coulomb lattice gas version of the Villain representation for the 2D Coulomb gases [36,37] and is also related to the electric field representation of the Coulomb gas used by Aizenman and Fröhlich [32]. In the limit of large γ it is clear that the process X n will be dominated by paths which start at zero and then stay as close as possible to the value Q.…”

Section: A Other Formulation and Limit Of Highly Charged Boundariesmentioning

confidence: 99%

“…The first exact solutions of the one dimensional Coulomb fluid or gas are due to Lenard and Edwards [31] where the bulk properties of a pointlike model of ions was studied. The problem was then analyzed in a more mathematical context [32], and the peculiar dependence of the bulk free energy on the electric field applied to such a system was elucidated. Later the effective interactions between charged surfaces in this model was studied [33,34] in the presence of counter and co-ions and counter-ions only.…”

Section: One Dimensional Lattice Coulomb Fluid Modelmentioning

confidence: 99%

“…This phenomenon occurs in the ordinary continuum one dimensional Coulomb fluid without hard core interactions, the thermodynamic limit thus depends on the boundary term. Physically this is related to the long range nature of the one dimensional Coulomb interaction and in terms of field theory the ground states or θ-vacua depend on the boundary terms [32].…”

Section: A Other Formulation and Limit Of Highly Charged Boundariesmentioning

confidence: 99%

See 2 more Smart Citations

The one-dimensional Coulomb lattice fluid capacitor

Démery

Dean

Hammant³

et al. 2012

The Journal of Chemical Physics

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The one dimensional Coulomb lattice fluid in a capacitor configuration is studied. The model is formally exactly soluble via a transfer operator method within a field theoretic representation of the model. The only interactions present in the model are the one dimensional Coulomb interaction between cations and anions and the steric interaction imposed by restricting the maximal occupancy at any lattice site to one particle. Despite the simplicity of the model, a wide range of intriguing physical phenomena arise, some of which are strongly reminiscent of those seen in experiments and numerical simulations of three dimensional ionic liquid based capacitors. Notably we find regimes where over-screening and density oscillations are seen near the capacitor plates. The capacitance is also shown to exhibit strong oscillations as a function of applied voltage. It is also shown that the corresponding mean field theory misses most of these effects. The analytical results are confirmed by extensive numerical simulations.

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Section: A Other Formulation and Limit Of Highly Charged Boundariesmentioning

confidence: 99%

Section: One Dimensional Lattice Coulomb Fluid Modelmentioning

confidence: 99%

Section: A Other Formulation and Limit Of Highly Charged Boundariesmentioning

confidence: 99%

See 1 more Smart Citation

The one-dimensional Coulomb lattice fluid capacitor

Démery

Dean

Hammant³

et al. 2012

The Journal of Chemical Physics

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“…When the system is not in an electroneutral state, i.e. when the surface charges corresponding to the applied field are not exactly compensated by the counterions of the system, the physics of the system is subtly different and confinement phenomena between oppositely charged particles appear [8,9]. This confinement is directly related to the fact that the system is dielectric and non-conducting.…”

Section: Introductionmentioning

confidence: 99%

One-dimensional counterion gas between charged surfaces: Exact results compared with weak- and strong-coupling analyses

Dean

Horgan

Naji

et al. 2009

The Journal of Chemical Physics

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We evaluate exactly the statistical integral for an inhomogeneous one-dimensional ͑1D͒ counterion-only Coulomb gas between two charged boundaries and from this compute the effective interaction, or disjoining pressure, between the bounding surfaces. Our exact results are compared to the limiting cases of weak and strong couplings which are the same for 1D and three-dimensional ͑3D͒ systems. For systems with a large number of counterions it is found that the weak-coupling ͑mean-field͒ approximation for the disjoining pressure works perfectly and that fluctuations around the mean-field in 1D are much smaller than in 3D. In the case of few counterions it works less well and strong-coupling approximation performs much better as it takes into account properly the discreteness of the counterion charges.

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“…As a result, an unrestricted generalized Coulomb gas with V (r) ∝ r α is expected to have a high temperature Debye-screening phase if α < 1. The fact that α = 1 (the 1D genuine Coulomb potential) is the borderline is confirmed by several exact investigations [14] [15] showing that this system is always in the dipolar phase at any temperature. Our problem is a special case, with α = 1/3.…”

Section: Monopoles In Dimension 0+1mentioning

confidence: 65%

Monopoles in the Gauge Theory of the t-J Model

Mélin¹,

Douçot²

1996

J. Phys. I France

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We consider a RG approach for the plasma of magnetic monopoles of the Ioffe-Larkin approach to the t-J model. We first derive the interaction parameters of the 2+1 plasma of magnetic monopoles. The total charge along the time axis is constrained to be zero for each lattice plaquette. Under the one-plaquette approximation, the problem is equivalent to a one dimensional neutral plasma interacting via a potential V (t) ∼ t α , with α = 1/3. The plasma is in a dipolar phase if α ≥ 1 and a possibility of transition towards a Debye screening phase arises if α < 1, so that there exists a critical Fermi wave vector k * f such as the plasma is Debye screening if k f < k * f and confined if k f > k * f . The 2+1 dimensional problem is treated numerically. We show that k * f decreases and goes to zero as the number of colors increases. This suggests that the assumption of spin-charge decoupling within the slave-boson scheme is self-consistent at large enough values of N and small enough doping. Elsewhere, a confining force between spinons and antiholons appears, suggesting a transition to a Fermi liquid state.

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States of one-dimensional Coulomb systems as simple examples of ? vacua and confinement

Cited by 12 publications

References 22 publications

The one-dimensional Coulomb lattice fluid capacitor

The one-dimensional Coulomb lattice fluid capacitor

One-dimensional counterion gas between charged surfaces: Exact results compared with weak- and strong-coupling analyses

Monopoles in the Gauge Theory of the t-J Model

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