52 research outputs found
Deconfinement transition and dimensional cross-over in the 3D gauge Ising model
We present a high precision Monte Carlo study of the finite temperature
gauge theory in 2+1 dimensions. The duality with the 3D Ising spin model allows
us to use powerful cluster algorithms for the simulations. For temporal
extensions up to we obtain the inverse critical temperature with a
statistical accuracy comparable with the most accurate results for the bulk
phase transition of the 3D Ising model. We discuss the predictions of T. W.
Capehart and M.E. Fisher for the dimensional crossover from 2 to 3 dimensions.
Our precise data for the critical exponents and critical amplitudes confirm the
Svetitsky-Yaffe conjecture. We find deviations from Olesen's prediction for the
critical temperature of about 20%.Comment: latex file of 21 pages plus 1 ps figure. Minor corrections in the
figure. Text unchange
A Swendsen-Wang update algorithm for the Symanzik improved sigma model
We study a generalization of Swendsen-Wang algorithm suited for Potts models
with next-next-neighborhood interactions. Using the embedding technique
proposed by Wolff we test it on the Symanzik improved bidimensional non-linear
model. For some long range observables we find a little slowing down
exponent () that we interpret as an effect of the partial
frustration of the induced spin model.Comment: Self extracting archive fil
Comparison of Monte Carlo Results for the 3D Ising Interface Tension and Interface Energy with (Extrapolated) Series Expansions
We compare Monte Carlo results for the interface tension and interface energy
of the 3-dimensional Ising model with Pad\'e and inhomogeneous differential
approximants of the low temperature series that was recently extended by Arisue
to order in . The series is expected to suffer
from the roughening singularity at . The comparison with the
Monte Carlo data shows that the Pad\'e and inhomogeneous differential
approximants fail to improve the truncated series result of the interface
tension and the interface energy in the region around the roughening
transition. The Monte Carlo data show that the specific heat displays a peak in
the smooth phase. Neither the truncated series nor the Pad\'e approximants find
this peak. We also compare Monte Carlo data for the energy of the ASOS model
with the corresponding low temperature series that we extended to order
.Comment: 22 pages, 9 figures appended as 3 PS-files, preprints
CERN-TH.7029/93, MS-TPI-93-0
Dynamical Scaling from Multi-Scale Measurements
We present a new measure of the Dynamical Critical behavior: the "Multi-scale
Dynamical Exponent (MDE)"Comment: 9 pages,Latex, Request figures from [email protected]
Finite Size Scaling and Critical Exponents in Critical Relaxation
We simulate the critical relaxation process of the two-dimensional Ising
model with the initial state both completely disordered or completely ordered.
Results of a new method to measure both the dynamic and static critical
exponents are reported, based on the finite size scaling for the dynamics at
the early time. From the time-dependent Binder cumulant, the dynamical exponent
is extracted independently, while the static exponents and
are obtained from the time evolution of the magnetization and its higher
moments.Comment: 24 pages, LaTeX, 10 figure
Dynamic structure factor of the Ising model with purely relaxational dynamics
We compute the dynamic structure factor for the Ising model with a purely
relaxational dynamics (model A). We perform a perturbative calculation in the
expansion, at two loops in the high-temperature phase and at one
loop in the temperature magnetic-field plane, and a Monte Carlo simulation in
the high-temperature phase. We find that the dynamic structure factor is very
well approximated by its mean-field Gaussian form up to moderately large values
of the frequency and momentum . In the region we can investigate,
, , where is the correlation
length and the zero-momentum autocorrelation time, deviations are at
most of a few percent.Comment: 21 pages, 3 figure
Calculations of the dynamical critical exponent using the asymptotic series summation method
We consider how the Pad'e-Borel, Pad'e-Borel-Leroy, and conformal mapping
summation methods for asymptotic series can be used to calculate the dynamical
critical exponent for homogeneous and disordered Ising-like systems.Comment: 21 RevTeX pages, 2 figure
New Dynamic Monte Carlo Renormalization Group Method
The dynamical critical exponent of the two-dimensional spin-flip Ising model
is evaluated by a Monte Carlo renormalization group method involving a
transformation in time. The results agree very well with a finite-size scaling
analysis performed on the same data. The value of is
obtained, which is consistent with most recent estimates
On the behaviour of spatial Wilson loops in the high temperature phase of Lattice Gauge Theories
The behaviour of the space-like string tension in the high temperature phase
is studied. Data obtained in the gauge model in (2+1) dimensions are
compared with predictions of a simple model of a fluctuating flux tube with
finite thickness. It is shown that in the high temperature phase contributions
coming from the fluctuations of the flux tube vanish. As a consequence we also
show that in (2+1) dimensional gauge theories the thickness of the flux tube
coincides with the inverse of the deconfinement temperature.Comment: 16 pages, 4 ps-figures included, (Latex), DFTT 57/9
Nonequilibrium relaxation of the two-dimensional Ising model: Series-expansion and Monte Carlo studies
We study the critical relaxation of the two-dimensional Ising model from a
fully ordered configuration by series expansion in time t and by Monte Carlo
simulation. Both the magnetization (m) and energy series are obtained up to
12-th order. An accurate estimate from series analysis for the dynamical
critical exponent z is difficult but compatible with 2.2. We also use Monte
Carlo simulation to determine an effective exponent, z_eff(t) = - {1/8} d ln t
/d ln m, directly from a ratio of three-spin correlation to m. Extrapolation to
t = infinity leads to an estimate z = 2.169 +/- 0.003.Comment: 9 pages including 2 figure
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