623 research outputs found

### Multi-Overlap Simulations for Transitions between Reference Configurations

We introduce a new procedure to construct weight factors, which flatten the
probability density of the overlap with respect to some pre-defined reference
configuration. This allows one to overcome free energy barriers in the overlap
variable. Subsequently, we generalize the approach to deal with the overlaps
with respect to two reference configurations so that transitions between them
are induced. We illustrate our approach by simulations of the brainpeptide
Met-enkephalin with the ECEPP/2 energy function using the global-energy-minimum
and the second lowest-energy states as reference configurations. The free
energy is obtained as functions of the dihedral and the root-mean-square
distances from these two configurations. The latter allows one to identify the
transition state and to estimate its associated free energy barrier.Comment: 12 pages, (RevTeX), 14 figures, Phys. Rev. E, submitte

### Overlap Distribution of the Three-Dimensional Ising Model

We study the Parisi overlap probability density P_L(q) for the
three-dimensional Ising ferromagnet by means of Monte Carlo (MC) simulations.
At the critical point P_L(q) is peaked around q=0 in contrast with the double
peaked magnetic probability density. We give particular attention to the tails
of the overlap distribution at the critical point, which we control over up to
500 orders of magnitude by using the multi-overlap MC algorithm. Below the
critical temperature interface tension estimates from the overlap probability
density are given and their approach to the infinite volume limit appears to be
smoother than for estimates from the magnetization.Comment: 7 pages, RevTex, 9 Postscript figure

### Simulated-tempering approach to spin-glass simulations

After developing an appropriate iteration procedure for the determination of
the parameters, the method of simulated tempering has been successfully applied
to the 2D Ising spin glass. The reduction of the slowing down is comparable to
that of the multicanonical algorithm. Simulated tempering has, however, the
advantages to allow full vectorization of the programs and to provide the
canonical ensemble directly.Comment: 12 pages (LaTeX), 4 postscript figures, uufiles encoded, submitted to
Physical Review

### SU(2) potentials in quantum gravity

We present investigations of the potential between static charges from a
simulation of quantum gravity coupled to an SU(2) gauge field on $6^{3}\times
4$ and $8^{3}\times 4$ simplicial lattices. In the well-defined phase of the
gravity sector where geometrical expectation values are stable, we study the
correlations of Polyakov loops and extract the corresponding potentials between
a source and sink separated by a distance $R$. In the confined phase, the
potential has a linear form while in the deconfined phase, a screened Coulombic
behavior is found. Our results indicate that quantum gravitational effects do
not destroy confinement due to non-abelian gauge fields.Comment: 3 pages, contribution to Lattice 94 conference, uuencoded compressed
postscript fil

### Spin glass overlap barriers in three and four dimensions

For the Edwards-Anderson Ising spin-glass model in three and four dimensions
(3d and 4d) we have performed high statistics Monte Carlo calculations of those
free-energy barriers $F^q_B$ which are visible in the probability density
$P_J(q)$ of the Parisi overlap parameter $q$. The calculations rely on the
recently introduced multi-overlap algorithm. In both dimensions, within the
limits of lattice sizes investigated, these barriers are found to be
non-self-averaging and the same is true for the autocorrelation times of our
algorithm. Further, we present evidence that barriers hidden in $q$ dominate
the canonical autocorrelation times.Comment: 20 pages, Latex, 12 Postscript figures, revised version to appear in
Phys. Rev.

### About the Functional Form of the Parisi Overlap Distribution for the Three-Dimensional Edwards-Anderson Ising Spin Glass

Recently, it has been conjectured that the statistics of extremes is of
relevance for a large class of correlated system. For certain probability
densities this predicts the characteristic large $x$ fall-off behavior
$f(x)\sim\exp (-a e^x)$, $a>0$. Using a multicanonical Monte Carlo technique,
we have calculated the Parisi overlap distribution $P(q)$ for the
three-dimensional Edward-Anderson Ising spin glass at and below the critical
temperature, even where $P(q)$ is exponentially small. We find that a
probability distribution related to extreme order statistics gives an excellent
description of $P(q)$ over about 80 orders of magnitude.Comment: 4 pages RevTex, 3 figure

### Phase diagram of Regge quantum gravity coupled to SU(2) gauge theory

We analyze Regge quantum gravity coupled to SU(2) gauge theory on $4^3\times
2$, $6^{3}\times 4$ and $8^{3}\times 4$ simplicial lattices. It turns out that
the window of the well-defined phase of the gravity sector where geometrical
expectation values are stable extends to negative gravitational couplings as
well as to gauge couplings across the deconfinement phase transition. We study
the string tension from Polyakov loops, compare with the $\beta$-function of
pure gauge theory and conclude that a physical limit through scaling is
possible.Comment: RevTeX, 14 pages, 5 figures (2 eps, 3 tex), 2 table

### Determining the density of states for classical statistical models: A random walk algorithm to produce a flat histogram

We describe an efficient Monte Carlo algorithm using a random walk in energy
space to obtain a very accurate estimate of the density of states for classical
statistical models. The density of states is modified at each step when the
energy level is visited to produce a flat histogram. By carefully controlling
the modification factor, we allow the density of states to converge to the true
value very quickly, even for large systems. This algorithm is especially useful
for complex systems with a rough landscape since all possible energy levels are
visited with the same probability. In this paper, we apply our algorithm to
both 1st and 2nd order phase transitions to demonstrate its efficiency and
accuracy. We obtained direct simulational estimates for the density of states
for two-dimensional ten-state Potts models on lattices up to $200 \times 200$
and Ising models on lattices up to $256 \times 256$. Applying this approach to
a 3D $\pm J$ spin glass model we estimate the internal energy and entropy at
zero temperature; and, using a two-dimensional random walk in energy and
order-parameter space, we obtain the (rough) canonical distribution and energy
landscape in order-parameter space. Preliminary data suggest that the glass
transition temperature is about 1.2 and that better estimates can be obtained
with more extensive application of the method.Comment: 22 pages (figures included

### Multicanonical Multigrid Monte Carlo

To further improve the performance of Monte Carlo simulations of first-order
phase transitions we propose to combine the multicanonical approach with
multigrid techniques. We report tests of this proposition for the
$d$-dimensional $\Phi^4$ field theory in two different situations. First, we
study quantum tunneling for $d = 1$ in the continuum limit, and second, we
investigate first-order phase transitions for $d = 2$ in the infinite volume
limit. Compared with standard multicanonical simulations we obtain improvement
factors of several resp. of about one order of magnitude.Comment: 12 pages LaTex, 1 PS figure appended. FU-Berlin preprint FUB-HEP 9/9

### Flat histogram simulation of lattice polymer systems

We demonstrate the use of a new algorithm called the Flat Histogram sampling
algorithm for the simulation of lattice polymer systems. Thermodynamics
properties, such as average energy or entropy and other physical quantities
such as end-to-end distance or radius of gyration can be easily calculated
using this method. Ground-state energy can also be determined. We also explore
the accuracy and limitations of this method.
Key words: Monte Carlo algorithms, flat histogram sampling, HP model, lattice
polymer systemsComment: 7 RevTeX two-column page

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