306 research outputs found
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
Medium-range interactions and crossover to classical critical behavior
We study the crossover from Ising-like to classical critical behavior as a
function of the range R of interactions. The power-law dependence on R of
several critical amplitudes is calculated from renormalization theory. The
results confirm the predictions of Mon and Binder, which were obtained from
phenomenological scaling arguments. In addition, we calculate the range
dependence of several corrections to scaling. We have tested the results in
Monte Carlo simulations of two-dimensional systems with an extended range of
interaction. An efficient Monte Carlo algorithm enabled us to carry out
simulations for sufficiently large values of R, so that the theoretical
predictions could actually be observed.Comment: 16 pages RevTeX, 8 PostScript figures. Uses epsf.sty. Also available
as PostScript and PDF file at http://www.tn.tudelft.nl/tn/erikpubs.htm
Universality class of criticality in the restricted primitive model electrolyte
The 1:1 equisized hard-sphere electrolyte or restricted primitive model has
been simulated via grand-canonical fine-discretization Monte Carlo. Newly
devised unbiased finite-size extrapolation methods using temperature-density,
(T, rho), loci of inflections, Q = ^2/ maxima, canonical and C_V
criticality, yield estimates of (T_c, rho_c) to +- (0.04, 3)%. Extrapolated
exponents and Q-ratio are (gamma, nu, Q_c) = [1.24(3), 0.63(3); 0.624(2)] which
support Ising (n = 1) behavior with (1.23_9, 0.630_3; 0.623_6), but exclude
classical, XY (n = 2), SAW (n = 0), and n = 1 criticality with potentials
phi(r)>Phi/r^{4.9} when r \to \infty
Quantum spin chains with site dissipation
We use Monte Carlo simulations to study chains of Ising- and XY-spins with
dissipation coupling to the site variables. The phase diagram and critical
exponents of the dissipative Ising chain in a transverse magnetic field have
been computed previously, and here we consider a universal ratio of
susceptibilities. We furthermore present the phase diagram and exponents of the
dissipative XY-chain, which exhibits a second order phase transition. All our
results compare well with the predictions from a dissipative field
theory
Crossover phenomena in spin models with medium-range interactions and self-avoiding walks with medium-range jumps
We study crossover phenomena in a model of self-avoiding walks with
medium-range jumps, that corresponds to the limit of an -vector
spin system with medium-range interactions. In particular, we consider the
critical crossover limit that interpolates between the Gaussian and the
Wilson-Fisher fixed point. The corresponding crossover functions are computed
using field-theoretical methods and an appropriate mean-field expansion. The
critical crossover limit is accurately studied by numerical Monte Carlo
simulations, which are much more efficient for walk models than for spin
systems. Monte Carlo data are compared with the field-theoretical predictions
concerning the critical crossover functions, finding a good agreement. We also
verify the predictions for the scaling behavior of the leading nonuniversal
corrections. We determine phenomenological parametrizations that are exact in
the critical crossover limit, have the correct scaling behavior for the leading
correction, and describe the nonuniversal lscrossover behavior of our data for
any finite range.Comment: 43 pages, revte
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.
Criticality in one dimension with inverse square-law potentials
It is demonstrated that the scaled order parameter for ferromagnetic Ising
and three-state Potts chains with inverse-square interactions exhibits a
universal critical jump, in analogy with the superfluid density in helium
films. Renormalization-group arguments are combined with numerical simulations
of systems containing up to one million lattice sites to accurately determine
the critical properties of these models. In strong contrast with earlier work,
compelling quantitative evidence for the Kosterlitz--Thouless-like character of
the phase transition is provided.Comment: To appear in Phys. Rev. Let
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
Rejection-free Geometric Cluster Algorithm for Complex Fluids
We present a novel, generally applicable Monte Carlo algorithm for the
simulation of fluid systems. Geometric transformations are used to identify
clusters of particles in such a manner that every cluster move is accepted,
irrespective of the nature of the pair interactions. The rejection-free and
non-local nature of the algorithm make it particularly suitable for the
efficient simulation of complex fluids with components of widely varying size,
such as colloidal mixtures. Compared to conventional simulation algorithms,
typical efficiency improvements amount to several orders of magnitude
A Monte Carlo study of the three-dimensional Coulomb frustrated Ising ferromagnet
We have investigated by Monte-Carlo simulation the phase diagram of a
three-dimensional Ising model with nearest-neighbor ferromagnetic interactions
and small, but long-range (Coulombic) antiferromagnetic interactions. We have
developed an efficient cluster algorithm and used different lattice sizes and
geometries, which allows us to obtain the main characteristics of the
temperature-frustration phase diagram. Our finite-size scaling analysis
confirms that the melting of the lamellar phases into the paramgnetic phase is
driven first-order by the fluctuations. Transitions between ordered phases with
different modulation patterns is observed in some regions of the diagram, in
agreement with a recent mean-field analysis.Comment: 14 pages, 10 figures, submitted to Phys. Rev.
- …