316 research outputs found
Generating a checking sequence with a minimum number of reset transitions
Given a finite state machine M, a checking sequence is an input sequence that is guaranteed to lead to a failure if the implementation under test is faulty and has no more states than M. There has been much interest in the automated generation of a short checking sequence from a finite state machine. However, such sequences can contain reset transitions whose use can adversely affect both the cost of applying the checking sequence and the effectiveness of the checking sequence. Thus, we sometimes want a checking sequence with a minimum number of reset transitions rather than a shortest checking sequence. This paper describes a new algorithm for generating a checking sequence, based on a distinguishing sequence, that minimises the number of reset transitions used.This work was supported in part by Leverhulme Trust grant number F/00275/D, Testing State Based Systems, Natural Sciences and Engineering Research Council (NSERC) of Canada grant number RGPIN 976, and Engineering and Physical Sciences Research Council grant number GR/R43150, Formal Methods and Testing (FORTEST)
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
On the inequivalence of statistical ensembles
We investigate the relation between various statistical ensembles of finite
systems. If ensembles differ at the level of fluctuations of the order
parameter, we show that the equations of states can present major differences.
A sufficient condition for this inequivalence to survive at the thermodynamical
limit is worked out. If energy consists in a kinetic and a potential part, the
microcanonical ensemble does not converge towards the canonical ensemble when
the partial heat capacities per particle fulfill the relation
.Comment: 4 pages, 4 figure
Surface critical exponents at a uniaxial Lifshitz point
Using Monte Carlo techniques, the surface critical behaviour of
three-dimensional semi-infinite ANNNI models with different surface
orientations with respect to the axis of competing interactions is
investigated. Special attention is thereby paid to the surface criticality at
the bulk uniaxial Lifshitz point encountered in this model. The presented Monte
Carlo results show that the mean-field description of semi-infinite ANNNI
models is qualitatively correct. Lifshitz point surface critical exponents at
the ordinary transition are found to depend on the surface orientation. At the
special transition point, however, no clear dependency of the critical
exponents on the surface orientation is revealed. The values of the surface
critical exponents presented in this study are the first estimates available
beyond mean-field theory.Comment: 10 pages, 7 figures include
Transient backbending behavior in the Ising model with fixed magnetization
The physical origin of the backbendings in the equations of state of finite
but not necessarily small systems is studied in the Ising model with fixed
magnetization (IMFM) by means of the topological properties of the observable
distributions and the analysis of the largest cluster with increasing lattice
size. Looking at the convexity anomalies of the IMFM thermodynamic potential,
it is shown that the order of the transition at the thermodynamic limit can be
recognized in finite systems independently of the lattice size. General
statistical mechanics arguments and analytical calculations suggest that the
backbending in the caloric curve is a transient behaviour which should not
converge to a plateau in the thermodynamic limit, while the first order
transition is signalled by a discontinuity in other observables.Comment: 24 pages, 11 figure
Critical behavior at m-axial Lifshitz points: field-theory analysis and -expansion results
The critical behavior of d-dimensional systems with an n-component order
parameter is reconsidered at (m,d,n)-Lifshitz points, where a wave-vector
instability occurs in an m-dimensional subspace of . Our aim is
to sort out which ones of the previously published partly contradictory
-expansion results to second order in are
correct. To this end, a field-theory calculation is performed directly in the
position space of dimensions, using dimensional
regularization and minimal subtraction of ultraviolet poles. The residua of the
dimensionally regularized integrals that are required to determine the series
expansions of the correlation exponents and and of the
wave-vector exponent to order are reduced to single
integrals, which for general m=1,...,d-1 can be computed numerically, and for
special values of m, analytically. Our results are at variance with the
original predictions for general m. For m=2 and m=6, we confirm the results of
Sak and Grest [Phys. Rev. B {\bf 17}, 3602 (1978)] and Mergulh{\~a}o and
Carneiro's recent field-theory analysis [Phys. Rev. B {\bf 59},13954 (1999)].Comment: Latex file with one figure (eps-file). Latex file uses texdraw to
generate figures that are included in the tex
Boundary critical behavior at m-axial Lifshitz points for a boundary plane parallel to the modulation axes
The critical behavior of semi-infinite -dimensional systems with
-component order parameter and short-range interactions is
investigated at an -axial bulk Lifshitz point whose wave-vector instability
is isotropic in an -dimensional subspace of . The associated
modulation axes are presumed to be parallel to the surface, where . An appropriate semi-infinite model representing the
corresponding universality classes of surface critical behavior is introduced.
It is shown that the usual O(n) symmetric boundary term
of the Hamiltonian must be supplemented by one of the form involving a
dimensionless (renormalized) coupling constant . The implied boundary
conditions are given, and the general form of the field-theoretic
renormalization of the model below the upper critical dimension
is clarified. Fixed points describing the ordinary, special,
and extraordinary transitions are identified and shown to be located at a
nontrivial value if . The surface
critical exponents of the ordinary transition are determined to second order in
. Extrapolations of these expansions yield values of these
exponents for in good agreement with recent Monte Carlo results for the
case of a uniaxial () Lifshitz point. The scaling dimension of the surface
energy density is shown to be given exactly by , where
is the anisotropy exponent.Comment: revtex4, 31 pages with eps-files for figures, uses texdraw to
generate some graphs; to appear in PRB; v2: some references and additional
remarks added, labeling in figure 1 and some typos correcte
The Percolation Signature of the Spin Glass Transition
Magnetic ordering at low temperature for Ising ferromagnets manifests itself
within the associated Fortuin-Kasteleyn (FK) random cluster representation as
the occurrence of a single positive density percolating network. In this paper
we investigate the percolation signature for Ising spin glass ordering -- both
in short-range (EA) and infinite-range (SK) models -- within a two-replica FK
representation and also within the different Chayes-Machta-Redner two-replica
graphical representation. Based on numerical studies of the EA model in
three dimensions and on rigorous results for the SK model, we conclude that the
spin glass transition corresponds to the appearance of {\it two} percolating
clusters of {\it unequal} densities.Comment: 13 pages, 6 figure
Crossover and self-averaging in the two-dimensional site-diluted Ising model
Using the newly proposed probability-changing cluster (PCC) Monte Carlo
algorithm, we simulate the two-dimensional (2D) site-diluted Ising model. Since
we can tune the critical point of each random sample automatically with the PCC
algorithm, we succeed in studying the sample-dependent and the sample
average of physical quantities at each systematically. Using the
finite-size scaling (FSS) analysis for , we discuss the importance of
corrections to FSS both in the strong-dilution and weak-dilution regions. The
critical phenomena of the 2D site-diluted Ising model are shown to be
controlled by the pure fixed point. The crossover from the percolation fixed
point to the pure Ising fixed point with the system size is explicitly
demonstrated by the study of the Binder parameter. We also study the
distribution of critical temperature . Its variance shows the power-law
dependence, , and the estimate of the exponent is consistent
with the prediction of Aharony and Harris [Phys. Rev. Lett. {\bf 77}, 3700
(1996)]. Calculating the relative variance of critical magnetization at the
sample-dependent , we show that the 2D site-diluted Ising model
exhibits weak self-averaging.Comment: 6 pages including 6 eps figures, RevTeX, to appear in Phys. Rev.
A review of Monte Carlo simulations of polymers with PERM
In this review, we describe applications of the pruned-enriched Rosenbluth
method (PERM), a sequential Monte Carlo algorithm with resampling, to various
problems in polymer physics. PERM produces samples according to any given
prescribed weight distribution, by growing configurations step by step with
controlled bias, and correcting "bad" configurations by "population control".
The latter is implemented, in contrast to other population based algorithms
like e.g. genetic algorithms, by depth-first recursion which avoids storing all
members of the population at the same time in computer memory. The problems we
discuss all concern single polymers (with one exception), but under various
conditions: Homopolymers in good solvents and at the point, semi-stiff
polymers, polymers in confining geometries, stretched polymers undergoing a
forced globule-linear transition, star polymers, bottle brushes, lattice
animals as a model for randomly branched polymers, DNA melting, and finally --
as the only system at low temperatures, lattice heteropolymers as simple models
for protein folding. PERM is for some of these problems the method of choice,
but it can also fail. We discuss how to recognize when a result is reliable,
and we discuss also some types of bias that can be crucial in guiding the
growth into the right directions.Comment: 29 pages, 26 figures, to be published in J. Stat. Phys. (2011
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