239 research outputs found
Correction induced by irrelevant operators in the correlators of the 2d Ising model in a magnetic field
We investigate the presence of irrelevant operators in the 2d Ising model
perturbed by a magnetic field, by studying the corrections induced by these
operators in the spin-spin correlator of the model. To this end we perform a
set of high precision simulations for the correlator both along the axes and
along the diagonal of the lattice. By comparing the numerical results with the
predictions of a perturbative expansion around the critical point we find
unambiguous evidences of the presence of such irrelevant operators. It turns
out that among the irrelevant operators the one which gives the largest
correction is the spin 4 operator T^2 + \bar T^2 which accounts for the
breaking of the rotational invariance due to the lattice. This result agrees
with what was already known for the correlator evaluated exactly at the
critical point and also with recent results obtained in the case of the thermal
perturbation of the model.Comment: 28 pages, no figure
Finding critical points using improved scaling Ansaetze
Analyzing in detail the first corrections to the scaling hypothesis, we
develop accelerated methods for the determination of critical points from
finite size data. The output of these procedures are sequences of
pseudo-critical points which rapidly converge towards the true critical points.
In fact more rapidly than previously existing methods like the Phenomenological
Renormalization Group approach. Our methods are valid in any spatial
dimensionality and both for quantum or classical statistical systems. Having at
disposal fast converging sequences, allows to draw conclusions on the basis of
shorter system sizes, and can be extremely important in particularly hard cases
like two-dimensional quantum systems with frustrations or when the sign problem
occurs. We test the effectiveness of our methods both analytically on the basis
of the one-dimensional XY model, and numerically at phase transitions occurring
in non integrable spin models. In particular, we show how a new Homogeneity
Condition Method is able to locate the onset of the
Berezinskii-Kosterlitz-Thouless transition making only use of ground-state
quantities on relatively small systems.Comment: 16 pages, 4 figures. New version including more general Ansaetze
basically applicable to all case
Irrelevant operators in the two-dimensional Ising model
By using conformal-field theory, we classify the possible irrelevant
operators for the Ising model on the square and triangular lattices. We analyze
the existing results for the free energy and its derivatives and for the
correlation length, showing that they are in agreement with the conformal-field
theory predictions. Moreover, these results imply that the nonlinear scaling
field of the energy-momentum tensor vanishes at the critical point. Several
other peculiar cancellations are explained in terms of a number of general
conjectures. We show that all existing results on the square and triangular
lattice are consistent with the assumption that only nonzero spin operators are
present.Comment: 32 pages. Added comments and reference
Quenched bond dilution in two-dimensional Potts models
We report a numerical study of the bond-diluted 2-dimensional Potts model
using transfer matrix calculations. For different numbers of states per spin,
we show that the critical exponents at the random fixed point are the same as
in self-dual random-bond cases. In addition, we determine the multifractal
spectrum associated with the scaling dimensions of the moments of the spin-spin
correlation function in the cylinder geometry. We show that the behaviour is
fully compatible with the one observed in the random bond case, confirming the
general picture according to which a unique fixed point describes the critical
properties of different classes of disorder: dilution, self-dual binary
random-bond, self-dual continuous random bond.Comment: LaTeX file with IOP macros, 29 pages, 14 eps figure
Progress of the Felsenkeller shallow-underground accelerator for nuclear astrophysics
Low-background experiments with stable ion beams are an important tool for
putting the model of stellar hydrogen, helium, and carbon burning on a solid
experimental foundation. The pioneering work in this regard has been done by
the LUNA collaboration at Gran Sasso, using a 0.4 MV accelerator. In the
present contribution, the status of the project for a higher-energy underground
accelerator is reviewed. Two tunnels of the Felsenkeller underground site in
Dresden, Germany, are currently being refurbished for the installation of a 5
MV high-current Pelletron accelerator. Construction work is on schedule and
expected to complete in August 2017. The accelerator will provide intense, 50
uA, beams of 1H+, 4He+, and 12C+ ions, enabling research on astrophysically
relevant nuclear reactions with unprecedented sensitivity.Comment: Submitted to the Proceedings of Nuclei in the Cosmos XIV, 19-24 June
2016, Niigata/Japa
symmetry of the BKT transition and twisted boundary conditio n
Berezinskii-Kosterlitz-Thouless (BKT) transition, the transition of the 2D
sine-Gordon model, plays an important role in the low dimensional physics. We
relate the operator content of the BKT transition to that of the SU(2)
Wess-Zumino-Witten model, using twisted boundary conditions. With this method,
in order to determine the BKT critical point, we can use the level crossing of
the lower excitations than the periodic boundary case, thus the convergence to
the transition point is highly improved. Then we verify the efficiency of this
method by applying to the S=1,2 spin chains.Comment: LaTex2e,, 33 pages, 14 figures in eps file
Finite-size scaling corrections in two-dimensional Ising and Potts ferromagnets
Finite-size corrections to scaling of critical correlation lengths and free
energies of Ising and three-state Potts ferromagnets are analysed by numerical
methods, on strips of width sites of square, triangular and honeycomb
lattices. Strong evidence is given that the amplitudes of the ``analytical''
correction terms, , are identically zero for triangular-- and honeycomb
Ising systems. For Potts spins, our results are broadly consistent with this
lattice-dependent pattern of cancellations, though for correlation lengths
non-vanishing (albeit rather small) amplitudes cannot be entirely ruled out.Comment: 11 pages, LaTeX with Institute of Physics macros, 2 EPS figures; to
appear in Journal of Physics
Global Standards in Action: Insights from Anti-Money Laundering Regulation
As organizations have come under the increasing influence of global rules of all sorts, organization scholars have started studying the dynamics of global regulation. The purpose of this article is to identify and evaluate the contribution to this interdisciplinary field by the âStockholm Centre for Organisational Researchâ. The latterâs key proposition is that while global regulation often consists of voluntary best practice rules it can nevertheless become highly influential under certain conditions. We assess how innovative this approach is using as a benchmark the state of the art in another field of relevance to the study of global regulation, i.e. âInternational Relationsâ. Our discussion is primarily theoretical but we draw on the case of global anti-money laundering regulation to illustrate our arguments and for inspirations of how to further elaborate the approach
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