4,015 research outputs found
Crossover Behavior from Decoupled Criticality
We study the thermodynamic phase transition of a spin Hamiltonian comprising
two 3D magnetic sublattices. Each sublattice contains XY spins coupled by the
usual bilinear exchange, while spins in different sublattices only interact via
biquadratic exchange. This Hamiltonian is an effective model for XY magnets on
certain frustrated lattices such as body centered tetragonal. By performing a
cluster Monte Carlo simulation, we investigate the crossover from the 3D-XY
fixed point (decoupled sublattices) and find a systematic flow toward a
first-order transition without a separatrix or a new fixed point. This strongly
suggests that the correct asymptotic behavior is a first-order transition.Comment: 10 pages, 3 figures; added reference
On the Use of Finite-Size Scaling to Measure Spin-Glass Exponents
Finite-size scaling (FSS) is a standard technique for measuring scaling
exponents in spin glasses. Here we present a critique of this approach,
emphasizing the need for all length scales to be large compared to microscopic
scales. In particular we show that the replacement, in FSS analyses, of the
correlation length by its asymptotic scaling form can lead to apparently good
scaling collapses with the wrong values of the scaling exponents.Comment: RevTeX, 5 page
Generalization of the Fortuin-Kasteleyn transformation and its application to quantum spin simulations,
We generalize the Fortuin-Kasteleyn (FK) cluster representation of the
partition function of the Ising model to represent the partition function of
quantum spin models with an arbitrary spin magnitude in arbitrary dimensions.
This generalized representation enables us to develop a new cluster algorithm
for the simulation of quantum spin systems by the worldline Monte Carlo method.
Because the Swendsen-Wang algorithm is based on the FK representation, the new
cluster algorithm naturally includes it as a special case. As well as the
general description of the new representation, we present an illustration of
our new algorithm for some special interesting cases: the Ising model, the
antiferromagnetic Heisenberg model with , and a general Heisenberg model.
The new algorithm is applicable to models with any range of the exchange
interaction, any lattice geometry, and any dimensions.Comment: 46 pages, 10 figures, to appear in J.Stat.Phy
Dual Monte Carlo and Cluster Algorithms
We discuss the development of cluster algorithms from the viewpoint of
probability theory and not from the usual viewpoint of a particular model. By
using the perspective of probability theory, we detail the nature of a cluster
algorithm, make explicit the assumptions embodied in all clusters of which we
are aware, and define the construction of free cluster algorithms. We also
illustrate these procedures by rederiving the Swendsen-Wang algorithm,
presenting the details of the loop algorithm for a worldline simulation of a
quantum 1/2 model, and proposing a free cluster version of the
Swendsen-Wang replica method for the random Ising model. How the principle of
maximum entropy might be used to aid the construction of cluster algorithms is
also discussed.Comment: 25 pages, 4 figures, to appear in Phys.Rev.
Monte Carlo Simulation of the Three-dimensional Ising Spin Glass
We study the 3D Edwards-Anderson model with binary interactions by Monte
Carlo simulations. Direct evidence of finite-size scaling is provided, and the
universal finite-size scaling functions are determined. Using an iterative
extrapolation procedure, Monte Carlo data are extrapolated to infinite volume
up to correlation length \xi = 140. The infinite volume data are consistent
with both a continuous phase transition at finite temperature and an essential
singularity at finite temperature. An essential singularity at zero temperature
is excluded.Comment: 5 pages, 6 figures. Proceedings of the Workshop "Computer Simulation
Studies in Condensed Matter Physics XII", Eds. D.P. Landau, S.P. Lewis, and
H.B. Schuettler, (Springer Verlag, Heidelberg, Berlin, 1999
Random quantum magnets with broad disorder distribution
We study the critical behavior of Ising quantum magnets with broadly
distributed random couplings (J), such that , , for large (L\'evy flight statistics).
For sufficiently broad distributions, , the critical behavior
is controlled by a line of fixed points, where the critical exponents vary with
the L\'evy index, . In one dimension, with , we obtaind
several exact results through a mapping to surviving Riemann walks. In two
dimensions the varying critical exponents have been calculated by a numerical
implementation of the Ma-Dasgupta-Hu renormalization group method leading to
. Thus in the region , where the
central limit theorem holds for the broadness of the distribution is
relevant for the 2d quantum Ising model.Comment: 10pages, 13figures, final for
Global classical solutions for partially dissipative hyperbolic system of balance laws
This work is concerned with (-component) hyperbolic system of balance laws
in arbitrary space dimensions. Under entropy dissipative assumption and the
Shizuta-Kawashima algebraic condition, a general theory on the well-posedness
of classical solutions in the framework of Chemin-Lerner's spaces with critical
regularity is established. To do this, we first explore the functional space
theory and develop an elementary fact that indicates the relation between
homogeneous and inhomogeneous Chemin-Lerner's spaces. Then this fact allows to
prove the local well-posedness for general data and global well-posedness for
small data by using the Fourier frequency-localization argument. Finally, we
apply the new existence theory to a specific fluid model-the compressible Euler
equations with damping, and obtain the corresponding results in critical
spaces.Comment: 39 page
On Landau's prediction for large-scale fluctuation of turbulence energy dissipation
Kolmogorov's theory for turbulence in 1941 is based on a hypothesis that
small-scale statistics are uniquely determined by the kinematic viscosity and
the mean rate of energy dissipation. Landau remarked that the local rate of
energy dissipation should fluctuate in space over large scales and hence should
affect small-scale statistics. Experimentally, we confirm the significance of
this large-scale fluctuation, which is comparable to the mean rate of energy
dissipation at the typical scale for energy-containing eddies. The significance
is independent of the Reynolds number and the configuration for turbulence
production. With an increase of scale r above the scale of largest
energy-containing eddies, the fluctuation becomes to have the scaling r^-1/2
and becomes close to Gaussian. We also confirm that the large-scale fluctuation
affects small-scale statistics.Comment: 9 pages, accepted by Physics of Fluids (see http://pof.aip.org
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