2,155 research outputs found
Make life simple: unleash the full power of the parallel tempering algorithm
We introduce a new update scheme to systematically improve the efficiency of
parallel tempering simulations. We show that by adapting the number of sweeps
between replica exchanges to the canonical autocorrelation time, the average
round-trip time of a replica in temperature space can be significantly
decreased. The temperatures are not dynamically adjusted as in previous
attempts but chosen to yield a 50% exchange rate of adjacent replicas. We
illustrate the new algorithm with results for the Ising model in two and the
Edwards-Anderson Ising spin glass in three dimensionsComment: 4 pages, 5 figure
Fluctuation Pressure of a Stack of Membranes
We calculate the universal pressure constants of a stack of N membranes
between walls by strong-coupling theory. The results are in very good agreement
with values from Monte-Carlo simulations.Comment: Author Information under
http://www.physik.fu-berlin.de/~kleinert/institution.html Latest update of
paper also at http://www.physik.fu-berlin.de/~kleinert/31
Simplified Transfer Matrix Approach in the Two-Dimensional Ising Model with Various Boundary Conditions
A recent simplified transfer matrix solution of the two-dimensional Ising
model on a square lattice with periodic boundary conditions is generalized to
periodic-antiperiodic, antiperiodic-periodic and antiperiodic-antiperiodic
boundary conditions. It is suggested to employ linear combinations of the
resulting partition functions to investigate finite-size scaling. An exact
relation of such a combination to the partition function corresponding to
Brascamp-Kunz boundary conditions is found.Comment: Phys.Rev.E, to be publishe
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
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
Critical exponents of the classical Heisenberg ferromagnet
In a recent letter, R.G. Brown and M. Ciftan (Phys. Rev. Lett. 76, 1352, 1996) reported high precision Monte Carlo (MC) estimates of the static critical exponents of the classical 3D Heisenberg model, which stand in sharp contrast to values obtained by four independent approaches, namely by other recent high statistics MC simulations, high-temperature series analyses, field theoretical methods, and experimental studies. In reply to the above cited work we submitted this paper as a comment to Phys. Rev. Lett
High precision single-cluster Monte Carlo measurement of the critical exponents of the classical 3D Heisenberg model
We report measurements of the critical exponents of the classical
three-dimensional Heisenberg model on simple cubic lattices of size with
= 12, 16, 20, 24, 32, 40, and 48. The data was obtained from a few long
single-cluster Monte Carlo simulations near the phase transition. We compute
high precision estimates of the critical coupling , Binder's parameter
\nu,\beta / \nu, \eta\alpha / \nu$,
using extensively histogram reweighting and optimization techniques that allow
us to keep control over the statistical errors. Measurements of the
autocorrelation time show the expected reduction of critical slowing down at
the phase transition as compared to local update algorithms. This allows
simulations on significantly larger lattices than in previous studies and
consequently a better control over systematic errors in finite-size scaling
analyses.Comment: 4 pages, (contribution to the Lattice92 proceedings) 1 postscript
file as uufile included. Preprints FUB-HEP 21/92 and HLRZ 89/92. (note: first
version arrived incomplete due to mailer problems
Lattice Models of Quantum Gravity
Standard Regge Calculus provides an interesting method to explore quantum
gravity in a non-perturbative fashion but turns out to be a CPU-time demanding
enterprise. One therefore seeks for suitable approximations which retain most
of its universal features. The -Regge model could be such a desired
simplification. Here the quadratic edge lengths of the simplicial complexes
are restricted to only two possible values , with
, in close analogy to the ancestor of all lattice theories, the
Ising model. To test whether this simpler model still contains the essential
qualities of the standard Regge Calculus, we study both models in two
dimensions and determine several observables on the same lattice size. In order
to compare expectation values, e.g. of the average curvature or the Liouville
field susceptibility, we employ in both models the same functional integration
measure. The phase structure is under current investigation using mean field
theory and numerical simulation.Comment: 4 pages, 1 figure
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