2,519 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
Shape of crossover between mean-field and asymptotic critical behavior in a three-dimensional Ising lattice
Recent numerical studies of the susceptibility of the three-dimensional Ising
model with various interaction ranges have been analyzed with a crossover model
based on renormalization-group matching theory. It is shown that the model
yields an accurate description of the crossover function for the
susceptibility.Comment: 4 pages RevTeX + 3 PostScript figures. Uses epsf.sty and rotate.sty.
Final version; accepted for publication in Physics Letters
Nature of crossover from classical to Ising-like critical behavior
We present an accurate numerical determination of the crossover from
classical to Ising-like critical behavior upon approach of the critical point
in three-dimensional systems. The possibility to vary the Ginzburg number in
our simulations allows us to cover the entire crossover region. We employ these
results to scrutinize several semi-phenomenological crossover scaling functions
that are widely used for the analysis of experimental results. In addition we
present strong evidence that the exponent relations do not hold between
effective exponents.Comment: 4 pages RevTeX 3.0/3.1, 4 Encapsulated PostScript figures. Uses
epsf.sty. Also available as PDF file at
http://www.cond-mat.physik.uni-mainz.de/~luijten/erikpubs.htm
Large-N_f chiral transition in the Yukawa model
We investigate the finite-temperature behavior of the Yukawa model in which
fermions are coupled with a scalar field in the limit . Close to the chiral transition the model shows a crossover between
mean-field behavior (observed for ) and Ising behavior (observed
for any finite ). We show that this crossover is universal and related to
that observed in the weakly-coupled theory. It corresponds to the
renormalization-group flow from the unstable Gaussian fixed point to the stable
Ising fixed point. This equivalence allows us to use results obtained in field
theory and in medium-range spin models to compute Yukawa correlation functions
in the crossover regime
Geometric Cluster Algorithm for Interacting Fluids
We discuss a new Monte Carlo algorithm for the simulation of complex fluids.
This algorithm employs geometric operations to identify clusters of particles
that can be moved in a rejection-free way. It is demonstrated that this
geometric cluster algorithm (GCA) constitutes the continuum generalization of
the Swendsen-Wang and Wolff cluster algorithms for spin systems. Because of its
nonlocal nature, it is particularly well suited for the simulation of fluid
systems containing particles of widely varying sizes. The efficiency
improvement with respect to conventional simulation algorithms is a rapidly
growing function of the size asymmetry between the constituents of the system.
We study the cluster-size distribution for a Lennard-Jones fluid as a function
of density and temperature and provide a comparison between the generalized GCA
and the hard-core GCA for a size-asymmetric mixture with Yukawa-type couplings.Comment: To appear in "Computer Simulation Studies in Condensed-Matter Physics
XVII". Edited by D.P. Landau, S.P. Lewis and H.B. Schuettler. Springer,
Heidelberg, 200
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
- …