51,977 research outputs found

### 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

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