583 research outputs found
Optimized energy calculation in lattice systems with long-range interactions
We discuss an efficient approach to the calculation of the internal energy in
numerical simulations of spin systems with long-range interactions. Although,
since the introduction of the Luijten-Bl\"ote algorithm, Monte Carlo
simulations of these systems no longer pose a fundamental problem, the energy
calculation is still an O(N^2) problem for systems of size N. We show how this
can be reduced to an O(N logN) problem, with a break-even point that is already
reached for very small systems. This allows the study of a variety of, until
now hardly accessible, physical aspects of these systems. In particular, we
combine the optimized energy calculation with histogram interpolation methods
to investigate the specific heat of the Ising model and the first-order regime
of the three-state Potts model with long-range interactions.Comment: 10 pages, including 8 EPS figures. To appear in Phys. Rev. E. Also
available as PDF file at
http://www.cond-mat.physik.uni-mainz.de/~luijten/erikpubs.htm
Critical properties of the three-dimensional equivalent-neighbor model and crossover scaling in finite systems
Accurate numerical results are presented for the three-dimensional
equivalent-neighbor model on a cubic lattice, for twelve different interaction
ranges (coordination number between 18 and 250). These results allow the
determination of the range dependences of the critical temperature and various
critical amplitudes, which are compared to renormalization-group predictions.
In addition, the analysis yields an estimate for the interaction range at which
the leading corrections to scaling vanish for the spin-1/2 model and confirms
earlier conclusions that the leading Wegner correction must be negative for the
three-dimensional (nearest-neighbor) Ising model. By complementing these
results with Monte Carlo data for systems with coordination numbers as large as
52514, the full finite-size crossover curves between classical and Ising-like
behavior are obtained as a function of a generalized Ginzburg parameter. Also
the crossover function for the effective magnetic exponent is determined.Comment: Corrected shift of critical temperature and some typos. To appear in
Phys. Rev. E. 18 pages RevTeX, including 10 EPS figures. Also available as
PDF file at http://www.cond-mat.physik.uni-mainz.de/~luijten/erikpubs.htm
Crossover critical behavior in the three-dimensional Ising model
The character of critical behavior in physical systems depends on the range
of interactions. In the limit of infinite range of the interactions, systems
will exhibit mean-field critical behavior, i.e., critical behavior not affected
by fluctuations of the order parameter. If the interaction range is finite, the
critical behavior asymptotically close to the critical point is determined by
fluctuations and the actual critical behavior depends on the particular
universality class. A variety of systems, including fluids and anisotropic
ferromagnets, belongs to the three-dimensional Ising universality class. Recent
numerical studies of Ising models with different interaction ranges have
revealed a spectacular crossover between the asymptotic fluctuation-induced
critical behavior and mean-field-type critical behavior. In this work, we
compare these numerical results with a crossover Landau model based on
renormalization-group matching. For this purpose we consider an application of
the crossover Landau model to the three-dimensional Ising model without fitting
to any adjustable parameters. The crossover behavior of the critical
susceptibility and of the order parameter is analyzed over a broad range (ten
orders) of the scaled distance to the critical temperature. The dependence of
the coupling constant on the interaction range, governing the crossover
critical behavior, is discussedComment: 10 pages in two-column format including 9 figures and 1 table.
Submitted to J. Stat. Phys. in honor of M. E. Fisher's 70th birthda
Nonmonotonical crossover of the effective susceptibility exponent
We have numerically determined the behavior of the magnetic susceptibility
upon approach of the critical point in two-dimensional spin systems with an
interaction range that was varied over nearly two orders of magnitude. The full
crossover from classical to Ising-like critical behavior, spanning several
decades in the reduced temperature, could be observed. Our results convincingly
show that the effective susceptibility exponent gamma_eff changes
nonmonotonically from its classical to its Ising value when approaching the
critical point in the ordered phase. In the disordered phase the behavior is
monotonic. Furthermore the hypothesis that the crossover function is universal
is supported.Comment: 4 pages RevTeX 3.0/3.1, 5 Encapsulated PostScript figures. Uses
epsf.sty. Accepted for publication in Physical Review Letters. Also available
as PostScript and PDF file at http://www.tn.tudelft.nl/tn/erikpubs.htm
Classical-to-critical crossovers from field theory
We extent the previous determinations of nonasymptotic critical behavior of
Phys. Rev B32, 7209 (1985) and B35, 3585 (1987) to accurate expressions of the
complete classical-to-critical crossover (in the 3-d field theory) in terms of
the temperature-like scaling field (i.e., along the critical isochore) for : 1)
the correlation length, the susceptibility and the specific heat in the
homogeneous phase for the n-vector model (n=1 to 3) and 2) for the spontaneous
magnetization (coexistence curve), the susceptibility and the specific heat in
the inhomogeneous phase for the Ising model (n=1). The present calculations
include the seventh loop order of Murray and Nickel (1991) and closely account
for the up-to-date estimates of universal asymptotic critical quantities
(exponents and amplitude combinations) provided by Guida and Zinn-Justin [J.
Phys. A31, 8103 (1998)].Comment: 4 figs, 4 program documents in appendix, some corrections adde
Crossover scaling from classical to nonclassical critical behavior
We study the crossover between classical and nonclassical critical behaviors.
The critical crossover limit is driven by the Ginzburg number G. The
corresponding scaling functions are universal with respect to any possible
microscopic mechanism which can vary G, such as changing the range or the
strength of the interactions. The critical crossover describes the unique flow
from the unstable Gaussian to the stable nonclassical fixed point. The scaling
functions are related to the continuum renormalization-group functions. We show
these features explicitly in the large-N limit of the O(N) phi^4 model. We also
show that the effective susceptibility exponent is nonmonotonic in the
low-temperature phase of the three-dimensional Ising model.Comment: 5 pages, final version to appear in Phys. Rev.
First-order transition in the one-dimensional three-state Potts model with long-range interactions
The first-order phase transition in the three-state Potts model with
long-range interactions decaying as has been examined by
numerical simulations using recently proposed Luijten-Bl\"ote algorithm. By
applying scaling arguments to the interface free energy, the Binder's
fourth-order cumulant, and the specific heat maximum, the change in the
character of the transition through variation of parameter was
studied.Comment: 6 pages (containing 5 figures), to appear in Phys. Rev.
Screening in Ionic Systems: Simulations for the Lebowitz Length
Simulations of the Lebowitz length, , are reported
for t he restricted primitive model hard-core (diameter ) 1:1 electrolyte
for densi ties and .
Finite-size eff ects are elucidated for the charge fluctuations in various
subdomains that serve to evaluate . On extrapolation to the
bulk limit for the low-density expansions (Bekiranov and
Fisher, 1998) are seen to fail badly when (with ). At highe r densities rises above the Debye
length, \xi_{\text{D}} \prop to \sqrt{T/\rho}, by 10-30% (upto ); the variation is portrayed fairly well by generalized
Debye-H\"{u}ckel theory (Lee and Fisher, 19 96). On approaching criticality at
fixed or fixed , remains finite with
but displays a
weak entropy-like singularity.Comment: 4 pages 5 figure
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