20 research outputs found
Weak Randomness for large q-State Potts models in Two Dimensions
We have studied the effect of weak randomness on q-state Potts models for q >
4 by measuring the central charges of these models using transfer matrix
methods. We obtain a set of new values for the central charges and then show
that some of these values are related to one another by a factorization law.Comment: 8 pages, Latex, no figure
Scaling and finte-size-scaling in the two dimensional random-coupling Ising ferromagnet
It is shown by Monte Carlo method that the finite size scaling (FSS) holds in
the two dimensional random-coupled Ising ferromagnet. It is also demonstrated
that the form of universal FSS function constructed via novel FSS scheme
depends on the strength of the random coupling for strongly disordered cases.
Monte Carlo measurements of thermodynamic (infinite volume limit) data of the
correlation length () up to along with measurements of
the fourth order cumulant ratio (Binder's ratio) at criticality are reported
and analyzed in view of two competing scenarios. It is demonstrated that the
data are almost exclusively consistent with the scenario of weak universality.Comment: 9 pages, 4figuer
Numerical Results For The 2D Random Bond 3-state Potts Model
We present results of a numerical simulation of the 3-state Potts model with
random bond, in two dimension. In particular, we measure the critical exponent
associated to the magnetization and the specific heat. We also compare these
exponents with recent analytical computations.Comment: 9 pages, latex, 3 Postscript figure
The critical amplitude ratio of the susceptibility in the random-site two-dimensional Ising model
We present a new way of probing the universality class of the site-diluted
two-dimensional Ising model. We analyse Monte Carlo data for the magnetic
susceptibility, introducing a new fitting procedure in the critical region
applicable even for a single sample with quenched disorder. This gives us the
possibility to fit simultaneously the critical exponent, the critical amplitude
and the sample dependent pseudo-critical temperature. The critical amplitude
ratio of the magnetic susceptibility is seen to be independent of the
concentration of the empty sites for all investigated values of . At the same time the average effective exponent is found
to vary with the concentration , which may be argued to be due to
logarithmic corrections to the power law of the pure system. This corrections
are canceled in the susceptibility amplitude ratio as predicted by theory. The
central charge of the corresponding field theory was computed and compared well
with the theoretical predictions.Comment: 6 pages, 4 figure
Critical behaviour of the Random--Bond Ashkin--Teller Model, a Monte-Carlo study
The critical behaviour of a bond-disordered Ashkin-Teller model on a square
lattice is investigated by intensive Monte-Carlo simulations. A duality
transformation is used to locate a critical plane of the disordered model. This
critical plane corresponds to the line of critical points of the pure model,
along which critical exponents vary continuously. Along this line the scaling
exponent corresponding to randomness varies continuously
and is positive so that randomness is relevant and different critical behaviour
is expected for the disordered model. We use a cluster algorithm for the Monte
Carlo simulations based on the Wolff embedding idea, and perform a finite size
scaling study of several critical models, extrapolating between the critical
bond-disordered Ising and bond-disordered four state Potts models. The critical
behaviour of the disordered model is compared with the critical behaviour of an
anisotropic Ashkin-Teller model which is used as a refference pure model. We
find no essential change in the order parameters' critical exponents with
respect to those of the pure model. The divergence of the specific heat is
changed dramatically. Our results favor a logarithmic type divergence at
, for the random bond Ashkin-Teller and four state Potts
models and for the random bond Ising model.Comment: RevTex, 14 figures in tar compressed form included, Submitted to
Phys. Rev.
Magnetic critical behavior of two-dimensional random-bond Potts ferromagnets in confined geometries
We present a numerical study of 2D random-bond Potts ferromagnets. The model
is studied both below and above the critical value which discriminates
between second and first-order transitions in the pure system. Two geometries
are considered, namely cylinders and square-shaped systems, and the critical
behavior is investigated through conformal invariance techniques which were
recently shown to be valid, even in the randomness-induced second-order phase
transition regime Q>4. In the cylinder geometry, connectivity transfer matrix
calculations provide a simple test to find the range of disorder amplitudes
which is characteristic of the disordered fixed point. The scaling dimensions
then follow from the exponential decay of correlations along the strip. Monte
Carlo simulations of spin systems on the other hand are generally performed on
systems of rectangular shape on the square lattice, but the data are then
perturbed by strong surface effects. The conformal mapping of a semi-infinite
system inside a square enables us to take into account boundary effects
explicitly and leads to an accurate determination of the scaling dimensions.
The techniques are applied to different values of Q in the range 3-64.Comment: LaTeX2e file with Revtex, revised versio
Ising model on 3D random lattices: A Monte Carlo study
We report single-cluster Monte Carlo simulations of the Ising model on
three-dimensional Poissonian random lattices with up to 128,000 approx. 503
sites which are linked together according to the Voronoi/Delaunay prescription.
For each lattice size quenched averages are performed over 96 realizations. By
using reweighting techniques and finite-size scaling analyses we investigate
the critical properties of the model in the close vicinity of the phase
transition point. Our random lattice data provide strong evidence that, for the
available system sizes, the resulting effective critical exponents are
indistinguishable from recent high-precision estimates obtained in Monte Carlo
studies of the Ising model and \phi^4 field theory on three-dimensional regular
cubic lattices.Comment: 35 pages, LaTex, 8 tables, 8 postscript figure
Rare region effects at classical, quantum, and non-equilibrium phase transitions
Rare regions, i.e., rare large spatial disorder fluctuations, can
dramatically change the properties of a phase transition in a quenched
disordered system. In generic classical equilibrium systems, they lead to an
essential singularity, the so-called Griffiths singularity, of the free energy
in the vicinity of the phase transition. Stronger effects can be observed at
zero-temperature quantum phase transitions, at nonequilibrium phase
transitions, and in systems with correlated disorder. In some cases, rare
regions can actually completely destroy the sharp phase transition by smearing.
This topical review presents a unifying framework for rare region effects at
weakly disordered classical, quantum, and nonequilibrium phase transitions
based on the effective dimensionality of the rare regions. Explicit examples
include disordered classical Ising and Heisenberg models, insulating and
metallic random quantum magnets, and the disordered contact process.Comment: Topical review, 68 pages, 14 figures, final version as publishe