3,167 research outputs found
Universal Dynamics of Independent Critical Relaxation Modes
Scaling behavior is studied of several dominant eigenvalues of spectra of
Markov matrices and the associated correlation times governing critical slowing
down in models in the universality class of the two-dimensional Ising model. A
scheme is developed to optimize variational approximants of progressively
rapid, independent relaxation modes. These approximants are used to reduce the
variance of results obtained by means of an adaptation of a quantum Monte Carlo
method to compute eigenvalues subject to errors predominantly of statistical
nature. The resulting spectra and correlation times are found to be universal
up to a single, non-universal time scale for each model
Monte Carlo computation of correlation times of independent relaxation modes at criticality
We investigate aspects of universality of Glauber critical dynamics in two
dimensions. We compute the critical exponent and numerically corroborate
its universality for three different models in the static Ising universality
class and for five independent relaxation modes. We also present evidence for
universality of amplitude ratios, which shows that, as far as dynamic behavior
is concerned, each model in a given universality class is characterized by a
single non-universal metric factor which determines the overall time scale.
This paper also discusses in detail the variational and projection methods that
are used to compute relaxation times with high accuracy
Monte Carlo Optimization of Trial Wave Functions in Quantum Mechanics and Statistical Mechanics
This review covers applications of quantum Monte Carlo methods to quantum
mechanical problems in the study of electronic and atomic structure, as well as
applications to statistical mechanical problems both of static and dynamic
nature. The common thread in all these applications is optimization of
many-parameter trial states, which is done by minimization of the variance of
the local or, more generally for arbitrary eigenvalue problems, minimization of
the variance of the configurational eigenvalue.Comment: 27 pages to appear in " Recent Advances in Quantum Monte Carlo
Methods" edited by W.A. Leste
Surface and bulk transitions in three-dimensional O(n) models
Using Monte Carlo methods and finite-size scaling, we investigate surface
criticality in the O models on the simple-cubic lattice with , 2, and
3, i.e. the Ising, XY, and Heisenberg models. For the critical couplings we
find and . We
simulate the three models with open surfaces and determine the surface magnetic
exponents at the ordinary transition to be ,
, and for , 2, and 3, respectively. Then we vary
the surface coupling and locate the so-called special transition at
and , where
. The corresponding surface thermal and magnetic exponents are
and for the Ising
model, and and for
the XY model. Finite-size corrections with an exponent close to -1/2 occur for
both models. Also for the Heisenberg model we find substantial evidence for the
existence of a special surface transition.Comment: TeX paper and 10 eps figure
Scaling in the vicinity of the four-state Potts fixed point
We study a self-dual generalization of the Baxter-Wu model, employing results
obtained by transfer matrix calculations of the magnetic scaling dimension and
the free energy. While the pure critical Baxter-Wu model displays the critical
behavior of the four-state Potts fixed point in two dimensions, in the sense
that logarithmic corrections are absent, the introduction of different
couplings in the up- and down triangles moves the model away from this fixed
point, so that logarithmic corrections appear. Real couplings move the model
into the first-order range, away from the behavior displayed by the
nearest-neighbor, four-state Potts model. We also use complex couplings, which
bring the model in the opposite direction characterized by the same type of
logarithmic corrections as present in the four-state Potts model. Our
finite-size analysis confirms in detail the existing renormalization theory
describing the immediate vicinity of the four-state Potts fixed point.Comment: 19 pages, 7 figure
Specific heat of the simple-cubic Ising model
We provide an expression quantitatively describing the specific heat of the
Ising model on the simple-cubic lattice in the critical region. This expression
is based on finite-size scaling of numerical results obtained by means of a
Monte Carlo method. It agrees satisfactorily with series expansions and with a
set of experimental results. Our results include a determination of the
universal amplitude ratio of the specific-heat divergences at both sides of the
critical point.Comment: 20 pages, 3 figure
Assessing satellite-derived land product quality for earth system science applications: results from the ceos lpv sub-group
The value of satellite derived land products for science applications and research is dependent upon the known accuracy of the data. CEOS (Committee on Earth Observation Satellites), the space arm of the Group on Earth Observations (GEO), plays a key role in coordinating the land product validation process. The Land Product Validation (LPV) sub-group of the CEOS Working Group on Calibration and Validation (WGCV) aims to address the challenges associated with the validation of global land products. This paper provides an overview of LPV sub-group focus area activities, which cover seven terrestrial Essential Climate Variables (ECVs). The contribution will enhance coordination of the scientific needs of the Earth system communities with global LPV activities
Transfer-matrix approach to the three-dimensional bond percolation: An application of Novotny's formalism
A transfer-matrix simulation scheme for the three-dimensional (d=3) bond
percolation is presented. Our scheme is based on Novotny's transfer-matrix
formalism, which enables us to consider arbitrary (integral) number of sites N
constituting a unit of the transfer-matrix slice even for d=3. Such an
arbitrariness allows us to perform systematic finite-size-scaling analysis of
the criticality at the percolation threshold. Diagonalizing the transfer matrix
for N =4,5,...,10, we obtain an estimate for the correlation-length critical
exponent nu = 0.81(5)
Critical line of an n-component cubic model
We consider a special case of the n-component cubic model on the square
lattice, for which an expansion exists in Ising-like graphs. We construct a
transfer matrix and perform a finite-size-scaling analysis to determine the
critical points for several values of n. Furthermore we determine several
universal quantities, including three critical exponents. For n<2, these
results agree well with the theoretical predictions for the critical O(n)
branch. This model is also a special case of the () model of
Domany and Riedel. It appears that the self-dual plane of the latter model
contains the exactly known critical points of the n=1 and 2 cubic models. For
this reason we have checked whether this is also the case for 1<n<2. However,
this possibility is excluded by our numerical results
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