501 research outputs found
Test of renormalization predictions for universal finite-size scaling functions
We calculate universal finite-size scaling functions for systems with an
n-component order parameter and algebraically decaying interactions. Just as
previously has been found for short-range interactions, this leads to a
singular epsilon-expansion, where epsilon is the distance to the upper critical
dimension. Subsequently, we check the results by numerical simulations of spin
models in the same universality class. Our systems offer the essential
advantage that epsilon can be varied continuously, allowing an accurate
examination of the region where epsilon is small. The numerical calculations
turn out to be in striking disagreement with the predicted singularity.Comment: 6 pages, including 3 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
Universal finite-size scaling analysis of Ising models with long-range interactions at the upper critical dimensionality: Isotropic case
We investigate a two-dimensional Ising model with long-range interactions
that emerge from a generalization of the magnetic dipolar interaction in spin
systems with in-plane spin orientation. This interaction is, in general,
anisotropic whereby in the present work we focus on the isotropic case for
which the model is found to be at its upper critical dimensionality. To
investigate the critical behavior the temperature and field dependence of
several quantities are studied by means of Monte Carlo simulations. On the
basis of the Privman-Fisher hypothesis and results of the renormalization group
the numerical data are analyzed in the framework of a finite-size scaling
analysis and compared to finite-size scaling functions derived from a
Ginzburg-Landau-Wilson model in zero mode (mean-field) approximation. The
obtained excellent agreement suggests that at least in the present case the
concept of universal finite-size scaling functions can be extended to the upper
critical dimensionality.Comment: revtex4, 10 pages, 5 figures, 1 tabl
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
A Geometrical Interpretation of Hyperscaling Breaking in the Ising Model
In random percolation one finds that the mean field regime above the upper
critical dimension can simply be explained through the coexistence of infinite
percolating clusters at the critical point. Because of the mapping between
percolation and critical behaviour in the Ising model, one might check whether
the breakdown of hyperscaling in the Ising model can also be intepreted as due
to an infinite multiplicity of percolating Fortuin-Kasteleyn clusters at the
critical temperature T_c. Preliminary results suggest that the scenario is much
more involved than expected due to the fact that the percolation variables
behave differently on the two sides of T_c.Comment: Lattice2002(spin
Stabilization of colloidal suspensions by means of highly-charged nanoparticles
We employ a novel Monte Carlo simulation scheme to elucidate the
stabilization of neutral colloidal microspheres by means of highly-charged
nanoparticles [V. Tohver et al., Proc. Natl. Acad. Sci. U.S.A. 98, 8950
(2001)]. In accordance with the experimental observations, we find that small
nanoparticle concentrations induce an effective repulsion that prevents
gelation caused by the intrinsic van der Waals attraction between colloids.
Higher nanoparticle concentrations induce an attractive potential which is,
however, qualitatively different from the regular depletion attraction. We also
show how colloid-nanoparticle size asymmetry and nanoparticle charge can be
used to manipulate the effective interactions.Comment: Accepted for publication in Physical Review Letters. See also S.
Karanikas and A.A. Louis, cond-mat/0411279. Updated to synchronize with
published versio
Percolation in high dimensions is not understood
The number of spanning clusters in four to nine dimensions does not fully
follow the expected size dependence for random percolation.Comment: 9-dimensional data and more points for large lattices added;
statistics improved, text expanded, table of exponents inserte
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
The true potential of artificial intelligence for detection of large-vessel occlusion:The role of M2 occlusions
Finite-size Scaling and Universality above the Upper Critical Dimensionality
According to renormalization theory, Ising systems above their upper critical
dimensionality d_u = 4 have classical critical behavior and the ratio of
magnetization moments Q = ^2 / has the universal value 0.456947...
However, Monte Carlo simulations of d = 5 Ising models have been reported which
yield strikingly different results, suggesting that the renormalization
scenario is incorrect. We investigate this issue by simulation of a more
general model in which d_u < 4, and a careful analysis of the corrections to
scaling. Our results are in a perfect agreement with the renormalization theory
and provide an explanation of the discrepancy mentioned.Comment: 5 pages RevTeX, 1 PostScript figure. Accepted for publication in
Physical Review Letter
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