2,730 research outputs found
Substrate Adhesion of a Nongrafted Flexible Polymer in a Cavity
In a contact density chain-growth study we investigate the
solubility-temperature pseudo-phase diagram of a lattice polymer in a cavity
with an attractive surface. In addition to the main phases of adsorbed and
desorbed conformations we find numerous subphases of collapsed and expanded
structures.Comment: 20 pages, 6 figure
Spacetime Approach to Phase Transitions
In these notes, the application of Feynman's sum-over-paths approach to
thermal phase transitions is discussed. The paradigm of such a spacetime
approach to critical phenomena is provided by the high-temperature expansion of
spin models. This expansion, known as the hopping expansion in the context of
lattice field theory, yields a geometric description of the phase transition in
these models, with the thermal critical exponents being determined by the
fractal structure of the high-temperature graphs. The graphs percolate at the
thermal critical point and can be studied using purely geometrical observables
known from percolation theory. Besides the phase transition in spin models and
in the closely related theory, other transitions discussed from this
perspective include Bose-Einstein condensation, and the transitions in the
Higgs model and the pure U(1) gauge theory.Comment: 59 pages, 18 figures. Write-up of Ising Lectures presented at the
National Academy of Sciences, Lviv, Ukraine, 2004. 2nd version: corrected
typo
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
Simplicial Quantum Gravity on a Randomly Triangulated Sphere
We study 2D quantum gravity on spherical topologies employing the Regge
calculus approach with the dl/l measure. Instead of the normally used fixed
non-regular triangulation we study random triangulations which are generated by
the standard Voronoi-Delaunay procedure. For each system size we average the
results over four different realizations of the random lattices. We compare
both types of triangulations quantitatively and investigate how the difference
in the expectation value of the squared curvature, , for fixed and random
triangulations depends on the lattice size and the surface area A. We try to
measure the string susceptibility exponents through finite-size scaling
analyses of the expectation value of an added -interaction term, using two
conceptually quite different procedures. The approach, where an ultraviolet
cut-off is held fixed in the scaling limit, is found to be plagued with
inconsistencies, as has already previously been pointed out by us. In a
conceptually different approach, where the area A is held fixed, these problems
are not present. We find the string susceptibility exponent in
rough agreement with theoretical predictions for the sphere, whereas the
estimate for appears to be too negative. However, our results
are hampered by the presence of severe finite-size corrections to scaling,
which lead to systematic uncertainties well above our statistical errors. We
feel that the present methods of estimating the string susceptibilities by
finite-size scaling studies are not accurate enough to serve as testing grounds
to decide about a success or failure of quantum Regge calculus.Comment: LaTex, 29 pages, including 9 figure
Simple flexible polymers in a spherical cage
We report the results of Monte Carlo simulations investigating the effect of
a spherical confinement within a simple model for a flexible homopolymer. We
use the parallel tempering method combined with multi-histogram reweighting
analysis and multicanonical simulations to investigate thermodynamical
observables over a broad range of temperatures, which enables us to describe
the behavior of the polymer and to locate the freezing and collapse
transitions. We find a strong effect of the spherical confinement on the
location of the collapse transition, whereas the freezing transition is hardly
effected.Comment: 7 pages, 4 figure
Error estimation and reduction with cross correlations
Besides the well-known effect of autocorrelations in time series of Monte
Carlo simulation data resulting from the underlying Markov process, using the
same data pool for computing various estimates entails additional cross
correlations. This effect, if not properly taken into account, leads to
systematically wrong error estimates for combined quantities. Using a
straightforward recipe of data analysis employing the jackknife or similar
resampling techniques, such problems can be avoided. In addition, a covariance
analysis allows for the formulation of optimal estimators with often
significantly reduced variance as compared to more conventional averages.Comment: 16 pages, RevTEX4, 4 figures, 6 tables, published versio
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