Screening in Ionic Systems: Simulations for the Lebowitz Length

Simulations of the Lebowitz length, $\xi_{\text{L}}(T,\rho)$, are reported for t he restricted primitive model hard-core (diameter $a$) 1:1 electrolyte for densi ties $\rho\lesssim 4\rho_c$ and $T_c \lesssim T \lesssim 40T_c$. Finite-size eff ects are elucidated for the charge fluctuations in various subdomains that serve to evaluate $\xi_{\text{L}}$. On extrapolation to the bulk limit for $T\gtrsim 10T_c$ the low-density expansions (Bekiranov and Fisher, 1998) are seen to fail badly when $\rho > {1/10}\rho_c$ (with $\rho_c a^3 \simeq 0.08$). At highe r densities $\xi_{\text{L}}$ rises above the Debye length, \xi_{\text{D}} \prop to \sqrt{T/\rho}, by 10-30% (upto $\rho\simeq 1.3\rho_c$); the variation is portrayed fairly well by generalized Debye-H\"{u}ckel theory (Lee and Fisher, 19 96). On approaching criticality at fixed $\rho$ or fixed $T$, $\xi_{\text{L}}(T, \rho)$ remains finite with $\xi_{\text{L}}^c \simeq 0.30 a \simeq 1.3 \xi_{\text {D}}^c$ but displays a weak entropy-like singularity.Comment: 4 pages 5 figure

Ferromagnetic Transition in One-Dimensional Itinerant Electron Systems

We use bosonization to derive the effective field theory that properly describes ferromagnetic transition in one-dimensional itinerant electron systems. The resultant theory is shown to have dynamical exponent z=2 at tree leve and upper critical dimension d_c=2. Thus one dimension is below the upper critical dimension of the theory, and the critical behavior of the transition is controlled by an interacting fixed point, which we study via epsilon expansion. Comparisons will be made with the Hertz-Millis theory, which describes the ferromagnetic transition in higher dimensions.Comment: 4 pages. Presentation improved. Final version as appeared in PR

Kinetic approach to the cluster liquid-gas transition

The liquid-gas transition in free atomic clusters is investigated theoretically based on simple unimolecular rate theories and assuming sequential evaporations. A kinetic Monte Carlo scheme is used to compute the time-dependent properties of clusters undergoing multiple dissociations, and two possible definitions of the boiling point are proposed, relying on the cluster or gas temperature. This numerical approach is supported by molecular dynamics simulations of clusters made of sodium atoms or C60 molecules, as well as simplified rate equation

From GM Law to A Powerful Mean Field Scheme

A new and powerful mean field scheme is presented. It maps to a one-dimensional finite closed chain in an external field. The chain size accounts for lattice topologies. Moreover lattice connectivity is rescaled according to the GM law recently obtained in percolation theory. The associated self-consistent mean-field equation of state yields critical temperatures which are within a few percent of exact estimates. Results are obtained for a large variety of lattices and dimensions. The Ising lower critical dimension for the onset of phase transitions is $d_l=1+\frac{2}{q}$. For the Ising hypercube it becomes the Golden number $d_l=\frac{1+\sqrt 5}{2}$. The scheme recovers the exact result of no long range order for non-zero temperature Ising triangular antiferromagnets.Comment: 3M Conference Proceedings, San Jose, California (November, 1999

On the finite-size behavior of systems with asymptotically large critical shift

Exact results of the finite-size behavior of the susceptibility in three-dimensional mean spherical model films under Dirichlet-Dirichlet, Dirichlet-Neumann and Neumann-Neumann boundary conditions are presented. The corresponding scaling functions are explicitly derived and their asymptotics close to, above and below the bulk critical temperature $T_c$ are obtained. The results can be incorporated in the framework of the finite-size scaling theory where the exponent $\lambda$ characterizing the shift of the finite-size critical temperature with respect to $T_c$ is smaller than $1/\nu$, with $\nu$ being the critical exponent of the bulk correlation length.Comment: 24 pages, late