1,679 research outputs found
2D Potts Model Correlation Lengths: Numerical Evidence for at
We have studied spin-spin correlation functions in the ordered phase of the
two-dimensional -state Potts model with , 15, and 20 at the
first-order transition point . Through extensive Monte Carlo
simulations we obtain strong numerical evidence that the correlation length in
the ordered phase agrees with the exactly known and recently numerically
confirmed correlation length in the disordered phase: . As a byproduct we find the energy moments in the ordered phase
at in very good agreement with a recent large -expansion.Comment: 11 pages, PostScript. To appear in Europhys. Lett. (September 1995).
See also http://www.cond-mat.physik.uni-mainz.de/~janke/doc/home_janke.htm
Monte Carlo Study of Cluster-Diameter Distribution: A New Observable to Estimate Correlation Lengths
We report numerical simulations of two-dimensional -state Potts models
with emphasis on a new quantity for the computation of spatial correlation
lengths. This quantity is the cluster-diameter distribution function
, which measures the distribution of the diameter of
stochastically defined cluster. Theoretically it is predicted to fall off
exponentially for large diameter , , where
is the correlation length as usually defined through the large-distance
behavior of two-point correlation functions. The results of our extensive Monte
Carlo study in the disordered phase of the models with , 15, and on
large square lattices of size , , and , respectively, clearly confirm the theoretically predicted behavior.
Moreover, using this observable we are able to verify an exact formula for the
correlation length in the disordered phase at the first-order
transition point with an accuracy of about for all considered
values of . This is a considerable improvement over estimates derived from
the large-distance behavior of standard (projected) two-point correlation
functions, which are also discussed for comparison.Comment: 20 pages, LaTeX + 13 postscript figures. See also
http://www.cond-mat.physik.uni-mainz.de/~janke/doc/home_janke.htm
Application of Multicanonical Multigrid Monte Carlo Method to the Two-Dimensional -Model: Autocorrelations and Interface Tension
We discuss the recently proposed multicanonical multigrid Monte Carlo method
and apply it to the scalar -model on a square lattice. To investigate
the performance of the new algorithm at the field-driven first-order phase
transitions between the two ordered phases we carefully analyze the
autocorrelations of the Monte Carlo process. Compared with standard
multicanonical simulations a real-time improvement of about one order of
magnitude is established. The interface tension between the two ordered phases
is extracted from high-statistics histograms of the magnetization applying
histogram reweighting techniques.Comment: 49 pp. Latex incl. 14 figures (Fig.7 not included, sorry) as
uuencoded compressed tar fil
Percolation of Vortices in the 3D Abelian Lattice Higgs Model
The compact Abelian Higgs model is simulated on a cubic lattice where it
possesses vortex lines and pointlike magnetic monopoles as topological defects.
The focus of this high-precision Monte Carlo study is on the vortex network,
which is investigated by means of percolation observables. In the region of the
phase diagram where the Higgs and confinement phases are separated by a
first-order transition, it is shown that the vortices percolate right at the
phase boundary, and that the first-order nature of the transition is reflected
by the network. In the crossover region, where the phase boundary ceases to be
first order, the vortices are shown to still percolate. In contrast to other
observables, the percolation observables show finite-size scaling. The
exponents characterizing the critical behavior of the vortices in this region
are shown to fall in the random percolation universality class.Comment: 24 pages, 12 figure
Thickness-dependent secondary structure formation of tubelike polymers
By means of sophisticated Monte Carlo methods, we investigate the
conformational phase diagram of a simple model for flexible polymers with
explicit thickness. The thickness constraint, which is introduced geometrically
via the global radius of curvature of a polymer conformation, accounts for the
excluded volume of the polymer and induces cooperative effects supporting the
formation of secondary structures. In our detailed analysis of the temperature
and thickness dependence of the conformational behavior for classes of short
tubelike polymers, we find that known secondary-structure segments like helices
and turns, but also ringlike conformations and stiff rods are dominant
intrinsic topologies governing the phase behavior of such cooperative tubelike
objects. This shows that the thickness constraint is indeed a fundamental
physical parameter that allows for a classification of generic polymer
structures
Two Anderson impurities in a 2D host with Rashba spin-orbit interaction
We have studied the two-dimensional two-impurity Anderson model with
additional Rashba spin-orbit interaction by means of the modified perturbation
theory. The impurity Green's functions we have constructed exactly reproduce
the first four spectral moments. We discuss the height and the width of the
even/odd Kondo peaks as functions of the inter-impurity distance and the Rashba
energy (the strength of the Rashba spin-orbit interaction). For small
impurity separations the Kondo temperature shows a non-monotonic dependence on
being different in the even and the odd channel. We predict that the
Kondo temperature has only almost linear dependence on and not an
exponential increase with Comment: To be published in Phys. Rev.
The Interface Tension in Quenched QCD at the Critical Temperature
We present results for the confinement-deconfinement interface tension
of quenched QCD. They were obtained by applying Binder's
histogram method to lattices of size for and
L=8,10,12\mbox{ and }14 with for and otherwise. The
use of a multicanonical algorithm and cylindrical geometries have turned out to
be crucial for the numerical studies.Comment: (talk presented by B. Grossmann at Lattice 92), 4 pages with 5 figure
appended as encapsulated postscript files at the end, preprint HLRZ-92-7
Monopole action from vacuum configurations in compact QED
It is possible to derive a monopole action from vacuum configurations
obtained in Monte-Carlo simulations extending the method developed by Swendsen.
We apply the method to compact QED both in the Villain and in the Wilson forms.
The action of the natural monopoles in the Villain case is in fairly good
agreement with that derived by the exact dual transformation. Comparing the
monopole actions, we find (1) the DeGrand-Toussaint monopole definition may be
useful for larger than about 0.5, (2) the Villain model well
approximates the Wilson one for smaller than and (3) in the
Wilson action the monopole condensation occurs in the confinement phase and
may be explained by the energy-entropy balance of monopole loops like
in the Villain case.Comment: 12 Pages+7 figures, KANAZAWA 94-1
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