Strong-coupling effective-field theory for asymmetrically charged plates with counterions only.

We are interested in rationalizing the phenomenon of like-charge attraction between charged bodies, such as a pair of colloids, in the strong coupling regime. The two colloids are modelled as uniformly charged parallel plates, neutralized by mobile counterions. In an earlier work [Palaia et al.

Ordered ground state configurations of the asymmetric Wigner bilayer system-Revisited with unsupervised learning.

We have reanalyzed the rich plethora of ground state configurations of the asymmetric Wigner bilayer system that we had recently published in a related diagram of states [Antlanger et al., Phys. Rev.

Ising ferromagnets and antiferromagnets in an imaginary magnetic field.

We study classical Ising spin-1/2 models on a two-dimensional (2D) square lattice with ferromagnetic or antiferromagnetic nearest-neighbor interactions, under the effect of a pure imaginary magnetic field. The complex Boltzmann weights of spin configurations cannot be interpreted as a probability distribution, which prevents application of standard statistical algorithms. In this work, the mapping of the Ising spin models under consideration onto symmetric vertex models leads to real (positive or negative) Boltzmann weights.

Like-Charge Attraction at the Nanoscale: Ground-State Correlations and Water Destructuring.

Like-charge attraction, driven by ionic correlations, challenges our understanding of electrostatics both in soft and hard matter. For two charged planar surfaces confining counterions and water, we prove that, even at relatively low correlation strength, the relevant physics is the ground-state one, oblivious of fluctuations. Based on this, we derive a simple and accurate interaction pressure that fulfills known exact requirements and can be used as an effective potential.

Strong-coupling theory of counterions with hard cores between symmetrically charged walls.

By a combination of Monte Carlo simulations and analytical calculations, we investigate the effective interactions between highly charged planar interfaces, neutralized by mobile counterions (salt-free system). While most previous analysis have focused on pointlike counterions, we treat them as charged hard spheres. We thus work out the fate of like-charge attraction when steric effects are at work.

Full nonuniversality of the symmetric 16-vertex model on the square lattice.

We consider the symmetric two-state 16-vertex model on the square lattice whose vertex weights are invariant under any permutation of adjacent edge states. The vertex-weight parameters are restricted to a critical manifold which is self-dual under the gauge transformation. The critical properties of the model are studied numerically with the Corner Transfer Matrix Renormalization Group method.

Electric double layers with surface charge modulations: Exact Poisson-Boltzmann solutions.

Poisson-Boltzmann theory is the cornerstone for soft matter electrostatics. We provide exact analytical solutions to this nonlinear mean-field approach for the diffuse layer of ions in the vicinity of a planar or a cylindrical macroion. While previously known solutions are for homogeneously charged objects, the cases worked out exhibit a modulated surface charge-or equivalently, surface potential-on the macroion (wall) surface.

The asymmetric Wigner bilayer.

We present a comprehensive discussion of the so-called asymmetric Wigner bilayer system, where mobile point charges, all of the same sign, are immersed into the space left between two parallel, homogeneously charged plates (with possibly different charge densities). At vanishing temperatures, the particles are expelled from the slab interior; they necessarily stick to one of the two plates and form there ordered sublattices. Using complementary tools (analytic and numerical), we study systematically the self-assembly of the point charges into ordered ground state configurations as the inter-layer separation and the asymmetry in the charge densities are varied.

Strong-coupling theory of counterions between symmetrically charged walls: from crystal to fluid phases.

We study thermal equilibrium of classical pointlike counterions confined between symmetrically charged walls at distance d. At very large couplings when the counterion system is in its crystal phase, a harmonic expansion of particle deviations is made around the bilayer positions, with a free lattice parameter determined from a variational approach. For each of the two walls, the harmonic expansion implies an effective one-body potential at the root of all observables of interest in our Wigner strong-coupling expansion.

Original electric-vertex formulation of the symmetric eight-vertex model on the square lattice is fully nonuniversal.

The partition function of the symmetric (zero electric field) eight-vertex model on a square lattice can be formulated either in the original "electric" vertex format or in an equivalent "magnetic" Ising-spin format. In this paper, both electric and magnetic versions of the model are studied numerically by using the corner transfer matrix renormalization-group method which provides reliable data. The emphasis is put on the calculation of four specific critical exponents, related by two scaling relations, and of the central charge.

Mean-field beyond mean-field: the single particle view for moderately to strongly coupled charged fluids.

In a counter-ion only charged fluid, Coulomb coupling is quantified by a single dimensionless parameter. Yet, the theoretical treatment of moderately to strongly coupled charged fluids is a difficult task, central to the understanding of a wealth of soft matter problems, including biological systems. We show that the corresponding coupling regime can be remarkably well described by a single particle treatment, which, at variance with previous works, takes due account of inter-ionic interactions.

Rich Polymorphic Behavior of Wigner Bilayers.

Self-assembly into target structures is an efficient material design strategy. Combining analytical calculations and computational techniques of evolutionary and Monte Carlo types, we report about a remarkable structural variability of Wigner bilayer ground states, when charges are confined between parallel charged plates. Changing the interlayer separation, or the plate charge asymmetry, a cascade of ordered patterns emerges.

Poisson-Boltzmann thermodynamics of counterions confined by curved hard walls.

We consider a set of identical mobile pointlike charges (counterions) confined to a domain with curved hard walls carrying a uniform fixed surface charge density, the system as a whole being electroneutral. Three domain geometries are considered: a pair of parallel plates, the cylinder, and the sphere. The particle system in thermal equilibrium is assumed to be described by the nonlinear Poisson-Boltzmann theory.

Reentrant disorder-disorder transitions in generalized multicomponent Widom-Rowlinson models.

In the lattice version of the multicomponent Widom-Rowlinson (WR) model, each site can be either empty or singly occupied by one of M different particles, all species having the same fugacity z. The only nonzero interaction potential is a nearest-neighbor hard-core exclusion between unlike particles. For Mz(d) (M).

Phase diagram and critical properties of Yukawa bilayers.

We study the ground-state Wigner bilayers of pointlike particles with Yukawa pairwise interactions, confined to the surface of two parallel hard walls at dimensionless distance η. The model involves as limiting cases the unscreened Coulomb potential and hard spheres. The phase diagram of Yukawa particles, studied numerically by Messina and Löwen [Phys.

Counter-ions at single charged wall: Sum rules.

For inhomogeneous classical Coulomb fluids in thermal equilibrium, like the jellium or the two-component Coulomb gas, there exists a variety of exact sum rules which relate the particle one-body and two-body densities. The necessary condition for these sum rules is that the Coulomb fluid possesses good screening properties, i.e.

Wigner-crystal formulation of strong-coupling theory for counterions near planar charged interfaces.

We present a new analytical approach to the strong electrostatic coupling regime (SC) that can be achieved equivalently at low temperatures, high charges, low dielectric permittivity, etc. Two geometries are analyzed in detail: one charged wall first, and then two parallel walls at small distances that can be likely or oppositely charged. In all cases, only one type of mobile counterions is present, and ensures electroneutrality (salt-free case).

Counterions at highly charged interfaces: from one plate to like-charge attraction.

We present an analytical approach for similarly and highly charged planar interfaces in the presence of counterions. The procedure is physically transparent and based on an exact low temperature expansion around the ground state formed by the two-dimensional Wigner crystal of counterions. The one plate problem is worked out, together with the two plates situation.

Equilibrium long-ranged charge correlations at the interface between media coupled to the electromagnetic radiation.

We continue studying long-ranged quantum correlations of surface charge densities on the interface between two media of distinct dielectric functions which are in thermal equilibrium with the radiated electromagnetic field. Two regimes are considered: the nonretarded one with the speed of light c taken to be infinitely large and the retarded one with a finite value of c . The analysis is based on our results obtained by using fluctuational electrodynamics [L.

Equilibrium long-ranged charge correlations at the surface of a conductor coupled to electromagnetic radiation. II.

Results of a previous paper with the same title are retrieved by a different method. A one-component plasma is bounded by a plane surface. The plasma is fully coupled to the electromagnetic field, therefore, the charge correlations are retarded.

Equilibrium long-ranged charge correlations at the surface of a conductor coupled to electromagnetic radiation.

This study is related to the fluctuation theory of electromagnetic fields, charges, and currents. The three-dimensional system under consideration is a semi-infinite conductor, modeled by the jellium, in vacuum. In previous theoretical studies it was found that the correlation functions of the surface charge density on the conductor decay as the inverse cube of the distance at asymptotically large distances.