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

We consider a general two-component plasma of classical pointlike charges \(+e\) (e is say the elementary charge) and \(-Z e\) (valency \(Z=1,2,\ldots \)), living on the surface of a sphere of radius R. The system is in thermal equilibrium at the inverse temperature \(\beta \), in the stability region against collapse of oppositely charged particle pairs \(\beta e^2 < 2/Z\). We study the effect of the system excess charge Qe on the finite-size expansion of the (dimensionless) grand potential \(\beta \varOmega \). 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 \(\beta e^2 < 2/Z\) the large-R expansion of the grand potential is of the form \(\beta \varOmega \sim A_V R^2 + \left[ \chi /6 - \beta (Qe)^2/2\right] \ln R\), where \(A_V\) is the non-universal coefficient of the volume (bulk) part and the Euler number of the sphere \(\chi =2\). The same formula, containing also a non-universal surface term proportional to R, was obtained previously for the disc domain (\(\chi =1\)), in the case of the symmetric \((Z=1)\) two-component plasma at the collapse point \(\beta e^2=2\) and the jellium model \((Z\rightarrow 0)\) of identical e-charges in a fixed neutralizing background charge density at any coupling \(\beta e^2\) 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 \(-\beta (Qe)^2/2\) is independent of the geometry of the confining domain.     

Heat Conductivity in a Two-Dimensional Finite-Size Spin System with Dzyaloshinskii-Moriya Interactions

Heat conductivity is studied by direct numerical simulations in a two-dimensional model with chiral Dzyaloshinskii-Moriya （DM） spin superexchange interactions for various DM strengths and finite sizes. We find that when temperature is not too low, the thermal conductivity can be well described in the semi-classical spin wave picture, and connections of thermal conductivity with the specific heat and the dynamic relaxation time are verified to be suitable. In particular, the transition arising in Sr14-xCaxCu24O41 is related to a magnetic spin glass and qualitatively understood as a kind of Kosterlitz-Thouless transitions. It is shown that the critical temperature is linearly dependent on the spin-spin interactions for the relevant strong DM strength.     

Logarithmic Corrections and Finite-Size Scaling in the Two-Dimensional 4-State Potts Model

We analyze the scaling and finite-size-scaling behavior of the two-dimensional 4-state Potts model. We find new multiplicative logarithmic corrections for the susceptibility, in addition to the already known ones for the specific heat. We also find additive logarithmic corrections to scaling, some of which are universal. We have checked the theoretical predictions at criticality and off criticality by means of high-precision Monte Carlo data.     

Density Correlations in the Two-Dimensional Coulomb Gas

We consider a two-dimensional Coulomb gas of positive and negative pointlike unit charges interacting via a logarithmic potential. The density (rather than the charge) correlation functions are studied. In the bulk, the form-factor theory of an equivalent sine-Gordon model is used to determine the density correlation length. At the surface of a rectilinear plain wall, the universality of the asymptotic behavior of the density correlations is suggested. A scaling analysis implies a local form of the compressibility sum rule near a hard wall. A symmetry of the Coulomb system with respect to the Möbius conformal transformation, which induces a gravitational source acting on the particle density, is established. Among the consequences, a universal term of the finite-size expansion of the grand potential is derived exactly for a disk geometry of the confining domain.     

Two-Dimensional Coulomb Plasmon-Excitons: Relaxation of Excitations

Physics of the Solid State - A theory is developed for the relaxation of two-dimensional non-radiative (Coulomb) plasmon-excitons in closely located thin layers of a metal and a semiconductor. In...     

Creep Motion in Two-Dimensional Fully Frustrated Coulomb Gas Model

The creep motion in a two-dimensional fully frustrated square lattice Coulomb gas model with disorders is studied by using the Monte Carlo technique. The dependence of charge current density J on electric field E is investigated at low temperature T and at low E. The results show that the creep obeys the Arrhenius law J - C（T） exp[-U（E）/T]. The prefactor C（T） increases with the temperature in a power law relation with an exponent about 3.0. The energy barrier U （ E） increases logarithmically with Ec,/ E as U （ E） - Uo ln（ Ec/ E） with Ec being the critical field at zero temperature.     

Exact Solution of a Charge-Asymmetric Two-Dimensional Coulomb Gas

The model under consideration is an asymmetric two-dimensional Coulomb gas of positively (q ₁=+1) and negatively (q ₂=–1/2) charged pointlike particles, interacting via a logarithmic potential. This continuous system is stable against collapse of positive-negative pairs of charges for the dimensionless coupling constant (inverse temperature) <4. The mapping of the Coulomb gas is made onto the complex Bullough–Dodd model, and recent results about that integrable 2D field theory are used. The mapping provides the full thermodynamics (the free energy, the internal energy, the specific heat) and the large-distance asymptotics of the particle correlation functions, in the whole stability regime of the plasma. The results are checked by a small- expansion and close to the collapse =4 point. The comparison is made with the exactly solvable symmetric version of the model (q ₁=+1,q ₂=–1), and some fundamental changes in statistics caused by the charge asymmetry are pointed out.     

Absorption Lineshapes in Two-Dimensional Electron Spin Resonance and the Effects of Slow Motions in Complex Fluids

A methodology for obtaining pure absorption two-dimensional electron spin resonance spectra is presented for the case of large inhomogeneous broadening and/or slow motions. For slow motions, the spectra consist of “complex Lorentzians” superimposed with complex weighting factors, presenting a challenge to obtaining absorption spectra. It is shown how absorption-type spectra can be recovered for the two-pulse COSY and SECSY experiments in such cases. For three-pulse 2D ELDOR experiments, absorption lineshapes can be obtained for the autopeaks, whereas the cross peaks would be of mixed-mode character, in general. However, for practical cases the dispersive components in the cross peaks will be relatively small. Theoretical and experimental absorption spectra are provided to illustrate the method and to show the improved resolution obtained from absorption lineshapes. In particular, the variation in linewidths across a SECSY spectrum, which is a key component in elucidating motional dynamics, is clearly rendered in the pure absorption mode. A convenient method for introducing the necessary phase corrections for the slow-motional spectra is also provided.     

Two-Dimensional Coulomb Systems in a Disk with Ideal Dielectric Boundaries

We study two-dimensional Coulomb systems confined in a disk with ideal dielectric boundaries. In particular we consider the two-component plasma in detail. When the coulombic coupling constant =2 the model is exactly solvable. We compute the grand potential, densities and correlations. We show that the grand potential has a universal logarithmic finite-size correction as predicted in previous works. This logarithmic finite-size correction is also found in the free energy of another solvable model: the one-component plasma.     

Two-Dimensional Rayleigh-Taylor Instability in Incompressible Fluids at Arbitrary Atwood Numbers

The Rayleigh-Taylor instability in two-dimensional incompressible fluids at arbitrary Atwood numbers is studied by expanding the perturbation velocity potential to third order. The second and third harmonic generation effects of single-mode perturbation are analyzed, as well as the nonlinear correction to the exponential growth of the fundamental modulation. The mode coupling coefficients are dependent on the Atwood numbers. Our simulations support the weakly nonlinear results. We find that the ratio of the nonlinear saturation amplitude ηs and the perturbation wavelength λ is dependent on the Atwood number AT and the relation is ηs/λ=（1/π）[√2/5/√（1＋3AT2 ）].     

Thermodynamic Properties of the Two-Dimensional Coulomb Gas in the Low-Density Limit

The model under consideration is the two-dimensional Coulomb gas of ± charged hard disks with diameter . For the case of pointlike charges (=0), the system is stable against collapse of positive-negative pairs of charges in the range of inverse temperatures 0<2, where its full exact thermodynamics was obtained recently. In the present work, we derive the leading correction to the exact thermodynamics of pointlike charges due to presence of the hard core which enables us to extend the treatment beyond the collapse point =2. Our results, which are conjectured to be exact in the low-density limit in the interval 0<3, reproduce correctly the singularities of thermodynamic quantities at the collapse point and agree well with Monte-Carlo simulations. The subtraction mechanism within the ansatz proposed by M. E. Fisher et al. [J. Stat. Phys. 79:1 (1995)], which excludes the existence of intermediate phases between the collapse point =2 and the Kosterlitz–Thouless transition point _KT=4, is confirmed, however, a different analytic structure of this ansatz is suggested.     

Guest Charge and Potential Fluctuations in Two-Dimensional Classical Coulomb Systems

A known generalization of the Stillinger-Lovett sum rule for a guest charge immersed in a two-dimensional one-component plasma (the second moment of the screening cloud around this guest charge) is more simply retrieved, just by using the BGY hierarchy for a mixture of several species; the zeroth moment of the excess density around a guest charge immersed in a two-component plasma is also obtained. The moments of the electric potential are related to the excess chemical potential of a guest charge; explicit results are obtained in several special cases. Unité Mixte de Recherche No. 8627—CNRS.     

Microscopic Calculation of the Dielectric Susceptibility Tensor for Coulomb Fluids

In a Coulomb fluid confined to a domain V, the dielectric susceptibility tensor _V depends on the shape of V, even in the thermodynamic V limit. This paper deals with the classical two-dimensional one-component plasma formulated in an elliptic V-domain, equilibrium statistical mechanics is used. For the dimensionless coupling constant =even positive integer, the mapping of the plasma onto a discrete one-dimensional anticommuting-field theory provides a new sum rule. This sum rule confirms the limiting value of _V predicted by macroscopic electrostatics and gives a finite-size correction term to _V.     

Two-Dimensional Coulomb Systems on a Surface of Constant Negative Curvature

We study the equilibrium statistical mechanics of classical two-dimensional Coulomb systems living on a pseudosphere (an infinite surface of constant negative curvature). The Coulomb potential created by one point charge exists and goes to zero at infinity. The pressure can be expanded as a series in integer powers of the density (the virial expansion). The correlation functions have a thermodynamic limit, and remarkably that limit is the same one for the Coulomb interaction and some other interaction law. However, special care is needed for defining a thermodynamic limit of the free energy density. There are sum rules expressing the property of perfect screening. These generic properties can be checked on the Debye–Hückel approximation, and on two exactly solvable models, the one-component plasma and the two-component plasma, at some special temperature.     

Renormalization Group Flow¶of the Two-Dimensional Hierarchical Coulomb Gas

We consider a quasilinear parabolic differential equation associated with the renormalization group transformation of the two-dimensional hierarchical Coulomb system in the limit as the size of the block L&\darr; 1. We show that the initial value problem is well defined in a suitable function space and the solution converges, as t→∞, to one of the countably infinite equilibrium solutions. The j ^th nontrivial equilibrium solution bifurcates from the trivial one at . These solutions are fully described and we provide a complete analysis of their local and global stability for all values of inverse temperature β >0. Gallavotti and Nicoló's conjecture on infinite sequence of “phases transitions” is also addressed. Our results rule out an intermediate phase between the plasma and the Kosterlitz–Thouless phases, at least in the hierarchical model we consider. Received: 29 November 1999 / Accepted: 13 January 2001     

Finite-Size Effects for Anisotropic Bootstrap Percolation: Logarithmic Corrections

In this note we analyse an anisotropic, two-dimensional bootstrap percolation model introduced by Gravner and Griffeath. We present upper and lower bounds on the finite-size effects. We discuss the similarities with the semi-oriented model introduced by Duarte.     

Phase Structure of Strongly Interacting Theories and Finite-Size Effects

Strongly interacting theories of fermions are of great interest both experimentally and theoretically. While heavy-ion collision experiments provide us with information on hot and dense QCD, experiments with ultracold trapped atoms provide an accessible and controllable system where quantum many-body phenomena can be studied experimentally in great detail. Our theoretical understanding of these theories has improved in recent years. However, finite-size effects in these systems are not yet fully understood. We review some aspects related to finite-size effects and the role that these effects are playing in strongly-interacting fermionic theories.     

Two-Dimensional Coulomb Glass as a Model for Vortex Pinning in Superconducting Films

A glass model of vortex pinning in highly disordered thin superconducting films in magnetic fields B ≪ H_c2 at low temperatures is proposed. Strong collective pinning of a vortex system realized in disordered superconductors that are close to the quantum phase transition to the insulating phase, such as InO_x, NbN, TiN, MoGe, and nanogranular aluminum, is considered theoretically for the first time. Utilizing the replica trick developed for the spin glass theory, we demonstrate that such vortex system is in non-ergodic state of glass type with a large kinetic inductance per square L_K. The distribution function of local pinning energies is calculated, and it is shown that it possesses a wide gap; i.e., the probability to find a weakly pinned vortex is extremely low.

     

Equation of State in the Fugacity Format for the Two-Dimensional Coulomb Gas

We derive the general form of the equation of state, in the fugacity format, for the two-dimensional Coulomb gas. Our results are valid in the conducting phase of the Coulomb gas, for temperatures above the Kosterlitz–Thouless transition. The derivation of the equation of state is based on the knowledge of the general form of the short-distance expansion of the correlation functions of the Coulomb gas. We explicitly compute the expansion up to order in the activity ζ. Our results are in very good agreement with Monte Carlo simulations at very low density.