1,710 research outputs found
Boundary field induced first-order transition in the 2D Ising model: numerical study
In a recent paper, Clusel and Fortin [J. Phys. A.: Math. Gen. 39 (2006) 995]
presented an analytical study of a first-order transition induced by an
inhomogeneous boundary magnetic field in the two-dimensional Ising model. They
identified the transition that separates the regime where the interface is
localized near the boundary from the one where it is propagating inside the
bulk. Inspired by these results, we measured the interface tension by using
multimagnetic simulations combined with parallel tempering to determine the
phase transition and the location of the interface. Our results are in very
good agreement with the theoretical predictions. Furthermore, we studied the
spin-spin correlation function for which no analytical results are available.Comment: 12 pages, 7 figures, 2 table
Multifractality of self-avoiding walks on percolation clusters
We consider self-avoiding walks (SAWs) on the backbone of percolation
clusters in space dimensions d=2, 3, 4. Applying numerical simulations, we show
that the whole multifractal spectrum of singularities emerges in exploring the
peculiarities of the model. We obtain estimates for the set of critical
exponents, that govern scaling laws of higher moments of the distribution of
percolation cluster sites visited by SAWs, in a good correspondence with an
appropriately summed field-theoretical \varepsilon=6-d-expansion (H.-K. Janssen
and O. Stenull, Phys. Rev. E 75, 020801(R) (2007)).Comment: 4 page
Cross-correlations in scaling analyses of phase transitions
Thermal or finite-size scaling analyses of importance sampling Monte Carlo
time series in the vicinity of phase transition points often combine different
estimates for the same quantity, such as a critical exponent, with the intent
to reduce statistical fluctuations. We point out that the origin of such
estimates in the same time series results in often pronounced
cross-correlations which are usually ignored even in high-precision studies,
generically leading to significant underestimation of statistical fluctuations.
We suggest to use a simple extension of the conventional analysis taking
correlation effects into account, which leads to improved estimators with often
substantially reduced statistical fluctuations at almost no extra cost in terms
of computation time.Comment: 4 pages, RevTEX4, 3 tables, 1 figur
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
Free zero-range processes on networks
A free zero-range process (FRZP) is a simple stochastic process describing
the dynamics of a gas of particles hopping between neighboring nodes of a
network. We discuss three different cases of increasing complexity: (a) FZRP on
a rigid geometry where the network is fixed during the process, (b) FZRP on a
random graph chosen from a given ensemble of networks, (c) FZRP on a dynamical
network whose topology continuously changes during the process in a way which
depends on the current distribution of particles. The case (a) provides a very
simple realization of the phenomenon of condensation which manifests as the
appearance of a condensate of particles on the node with maximal degree. The
case (b) is very interesting since the averaging over typical ensembles of
graphs acts as a kind of homogenization of the system which makes all nodes
identical from the point of view of the FZRP. In the case (c), the distribution
of particles and the dynamics of network are coupled to each other. The
strength of this coupling depends on the ratio of two time scales: for changes
of the topology and of the FZRP. We will discuss a specific example of that
type of interaction and show that it leads to an interesting phase diagram.Comment: 11 pages, 4 figures, to appear in Proceedings of SPIE Symposium
"Fluctuations and Noise 2007", Florence, 20-24 May 200
Multicanonical Study of Coarse-Grained Off-Lattice Models for Folding Heteropolymers
We have performed multicanonical simulations of hydrophobic-hydrophilic
heteropolymers with two simple effective, coarse-grained off-lattice models to
study the influence of specific interactions in the models on conformational
transitions of selected sequences with 20 monomers. Another aspect of the
investigation was the comparison with the purely hydrophobic homopolymer and
the study of general conformational properties induced by the "disorder" in the
sequence of a heteropolymer. Furthermore, we applied an optimization algorithm
to sequences with up to 55 monomers and compared the global-energy minimum
found with lowest-energy states identified within the multicanonical
simulation. This was used to find out how reliable the multicanonical method
samples the free-energy landscape, in particular for low temperatures.Comment: 11 pages, RevTeX, 10 Postscript figures, Author Information under
http://www.physik.uni-leipzig.de/index.php?id=2
Balls-in-boxes condensation on networks
We discuss two different regimes of condensate formation in zero-range
processes on networks: on a q-regular network, where the condensate is formed
as a result of a spontaneous symmetry breaking, and on an irregular network,
where the symmetry of the partition function is explicitly broken. In the
latter case we consider a minimal irregularity of the q-regular network
introduced by a single Q-node with degree Q>q. The statics and dynamics of the
condensation depends on the parameter log(Q/q), which controls the exponential
fall-off of the distribution of particles on regular nodes and the typical time
scale for melting of the condensate on the Q-node which increases exponentially
with the system size . This behavior is different than that on a q-regular
network where log(Q/q)=0 and where the condensation results from the
spontaneous symmetry breaking of the partition function, which is invariant
under a permutation of particle occupation numbers on the q-nodes of the
network. In this case the typical time scale for condensate melting is known to
increase typically as a power of the system size.Comment: 7 pages, 3 figures, submitted to the "Chaos" focus issue on
"Optimization in Networks" (scheduled to appear as Volume 17, No. 2, 2007
- …