Monte Carlo simulations of the screening potential of the Yukawa one-component plasma

A Monte Carlo scheme to sample the screening potential H(r) of Yukawa plasmas notably at short distances is presented. This scheme is based on an importance sampling technique. Comparisons with former results for the Coulombic one-component plasma are given. Our Monte Carlo simulations yield an accurate estimate of H(r) as well for short range and long range interparticle distances.Comment: to be published in Journal of Physics A: Mathematical and Genera

An accurate equation of state for the one component plasma in the low coupling regime

An accurate equation of state of the one component plasma is obtained in the low coupling regime $0 \leq \Gamma \leq 1$. The accuracy results from a smooth combination of the well-known hypernetted chain integral equation, Monte Carlo simulations and asymptotic analytical expressions of the excess internal energy $u$. In particular, special attention has been brought to describe and take advantage of finite size effects on Monte Carlo results to get the thermodynamic limit of $u$. This combined approach reproduces very accurately the different plasma correlation regimes encountered in this range of values of $\Gamma$. This paper extends to low $\Gamma$'s an earlier Monte Carlo simulation study devoted to strongly coupled systems for $1 \leq \Gamma \leq 190$ ({J.-M. Caillol}, {J. Chem. Phys.} \textbf{111}, 6538 (1999)). Analytical fits of $u(\Gamma)$ in the range $0 \leq \Gamma \leq 1$ are provided with a precision that we claim to be not smaller than $p= 10^{-5}$. HNC equation and exact asymptotic expressions are shown to give reliable results for $u(\Gamma)$ only in narrow $\Gamma$ intervals, i.e. $0 \leq \Gamma \lesssim 0.5$ and $0 \leq \Gamma \lesssim 0.3$ respectively

Low-Field Phase Diagram of Layered Superconductors: The Role of Electromagnetic Coupling

We determine the position and shape of the melting line in a layered superconductor taking the electromagnetic coupling between layers into account. In the limit of vanishing Josephson coupling we obtain a new generic reentrant low-field melting line. Finite Josephson coupling pushes the melting line to higher temperatures and fields and a new line shape $B_{{\rm m}} \propto (1-T/T_c)^{3/2}$ is found. We construct the low-field phase diagram including melting and decoupling lines and discuss various experiments in the light of our new results.Comment: 12 pages, 1 figure attached as compressed and uuencoded postscrip

Scalar Casimir Effect on a D-dimensional Einstein Static Universe

We compute the renormalised energy momentum tensor of a free scalar field coupled to gravity on an (n+1)-dimensional Einstein Static Universe (ESU), RxS^n, with arbitrary low energy effective operators (up to mass dimension n+1). A generic class of regulators is used, together with the Abel-Plana formula, leading to a manifestly regulator independent result. The general structure of the divergences is analysed to show that all the gravitational couplings (not just the cosmological constant) are renormalised for an arbitrary regulator. Various commonly used methods (damping function, point-splitting, momentum cut-off and zeta function) are shown to, effectively, belong to the given class. The final results depend strongly on the parity of n. A detailed analytical and numerical analysis is performed for the behaviours of the renormalised energy density and a quantity `sigma' which determines if the strong energy condition holds for the `quantum fluid'. We briefly discuss the quantum fluid back-reaction problem, via the higher dimensional Friedmann and Raychaudhuri equations, observe that equilibrium radii exist and unveil the possibility of a `Casimir stabilisation of Einstein Static Universes'.Comment: 37 pages, 15 figures, v2: minor changes in sections 1, 2.5, 3 and 4; version published in CQ

The density functional theory of classical fluids revisited

We reconsider the density functional theory of nonuniform classical fluids from the point of view of convex analysis. From the observation that the logarithm of the grand-partition function $\log \Xi [\phi]$ is a convex functional of the external potential $\phi$ it is shown that the Kohn-Sham free energy ${\cal A}[\rho]$ is a convex functional of the density $\rho$. $\log \Xi [\phi]$ and ${\cal A}[\rho]$ constitute a pair of Legendre transforms and each of these functionals can therefore be obtained as the solution of a variational principle. The convexity ensures the unicity of the solution in both cases. The variational principle which gives $\log \Xi [\phi]$ as the maximum of a functional of $\rho$ is precisely that considered in the density functional theory while the dual principle, which gives ${\cal A}[\rho]$ as the maximum of a functional of $\phi$ seems to be a new result.Comment: 10 page

Vortices in a Thin Film Superconductor with a Spherical Geometry

We report results from Monte Carlo simulations of a thin film superconductor in a spherical geometry within the lowest Landau level approximation. We observe the absence of a phase transition to a low temperature vortex solid phase with these boundary conditions; the system remains in the vortex liquid phase for all accessible temperatures. The correlation lengths are measured for phase coherence and density modulation. Both lengths display identical temperature dependences, with an asymptotic scaling form consistent with a continuous zero temperature transition. This contrasts with the first order freezing transition which is seen in the alternative quasi-periodic boundary conditions. The high temperature perturbation theory and the ground states of the spherical system suggest that the thermodynamic limit of the spherical geometry is the same as that on the flat plane. We discuss the advantages and drawbacks of simulations with different geometries, and compare with current experimental conclusions. The effect of having a large scale inhomogeneity in the applied field is also considered.Comment: This replacment contains substantial revisions: the new article is twice as long with new and different results on the thermodynamic limit on the sphere plus a full discussion on the alternative boundary conditions used in simulations in the LLL approximation. 19 pages, 12 encapsulated PostScript figures, 1 JPEG figure, uses RevTeX (with epsf

Absence of a Finite-Temperature Melting Transition in the Classical Two-Dimensional One-Component Plasma

Vortices in thin-film superconductors are often modelled as a system of particles interacting via a repulsive logarithmic potential. Arguments are presented to show that the hypothetical (Abrikosov) crystalline state for such particles is unstable at any finite temperature against proliferation of screened disclinations. The correlation length of crystalline order is predicted to grow as $\sqrt{1/T}$ as the temperature $T$ is reduced to zero, in excellent agreement with our simulations of this two-dimensional system.Comment: 3 figure

Evaporation of the pancake-vortex lattice in weakly-coupled layered superconductors

We calculate the melting line of the pancake-vortex system in a layered superconductor, interpolating between two-dimensional (2D) melting at high fields and the zero-field limit of single-stack evaporation. Long-range interactions between pancake vortices in different layers permit a mean-field approach, the ``substrate model'', where each 2D crystal fluctuates in a substrate potential due to the vortices in other layers. We find the thermal stability limit of the 3D solid, and compare the free energy to a 2D liquid to determine the first-order melting transition and its jump in entropy.Comment: 4 pages, RevTeX, two postscript figures incorporated using eps

Vortices and 2D bosons: A Path-Integral Monte Carlo Study

The vortex system in a high-T_c superconductor has been studied numerically using the mapping to 2D bosons and the path-integral Monte Carlo method. We find a single first-order transition from an Abrikosov lattice to an entangled vortex liquid. The transition is characterized by an entropy jump dS = 0.4 k_B per vortex and layer (parameters for YBCO) and a Lindemann number c_L = 0.25. The increase in density at melting is given by d\rho = 6.0*10^{-4} / \lambda(T)^2. The vortex liquid corresponds to a bosonic superfluid, with \rho_s = \rho even in the limit \lambda -> \infty.Comment: 9 pages, RevTeX, 4 PostScript figures. The entropy jump at the transition has been recomputed and is now in agreement with experiments on YBCO. Some minor modifications were made in the tex

Correlations in two-component log-gas systems

A systematic study of the properties of particle and charge correlation functions in the two-dimensional Coulomb gas confined to a one-dimensional domain is undertaken. Two versions of this system are considered: one in which the positive and negative charges are constrained to alternate in sign along the line, and the other where there is no charge ordering constraint. Both systems undergo a zero-density Kosterlitz-Thouless type transition as the dimensionless coupling $\Gamma := q^2 / kT$ is varied through $\Gamma = 2$. In the charge ordered system we use a perturbation technique to establish an $O(1/r^4)$ decay of the two-body correlations in the high temperature limit. For $\Gamma \rightarrow 2^+$, the low-fugacity expansion of the asymptotic charge-charge correlation can be resummed to all orders in the fugacity. The resummation leads to the Kosterlitz renormalization equations.Comment: 39 pages, 5 figures not included, Latex, to appear J. Stat. Phys. Shortened version of abstract belo