660 research outputs found
Monte Carlo Tests of SLE Predictions for the 2D Self-Avoiding Walk
The conjecture that the scaling limit of the two-dimensional self-avoiding
walk (SAW) in a half plane is given by the stochastic Loewner evolution (SLE)
with leads to explicit predictions about the SAW. A remarkable
feature of these predictions is that they yield not just critical exponents,
but probability distributions for certain random variables associated with the
self-avoiding walk. We test two of these predictions with Monte Carlo
simulations and find excellent agreement, thus providing numerical support to
the conjecture that the scaling limit of the SAW is SLE.Comment: TeX file using APS REVTeX 4.0. 10 pages, 5 figures (encapsulated
postscript
Surface Code Threshold in the Presence of Correlated Errors
We study the fidelity of the surface code in the presence of correlated
errors induced by the coupling of physical qubits to a bosonic environment. By
mapping the time evolution of the system after one quantum error correction
cycle onto a statistical spin model, we show that the existence of an error
threshold is related to the appearance of an order-disorder phase transition in
the statistical model in the thermodynamic limit. This allows us to relate the
error threshold to bath parameters and to the spatial range of the correlated
errors.Comment: 5 pages, 2 figure
Pattern theorems, ratio limit theorems and Gumbel maximal clusters for random fields
We study occurrences of patterns on clusters of size n in random fields on
Z^d. We prove that for a given pattern, there is a constant a>0 such that the
probability that this pattern occurs at most an times on a cluster of size n is
exponentially small. Moreover, for random fields obeying a certain Markov
property, we show that the ratio between the numbers of occurrences of two
distinct patterns on a cluster is concentrated around a constant value. This
leads to an elegant and simple proof of the ratio limit theorem for these
random fields, which states that the ratio of the probabilities that the
cluster of the origin has sizes n+1 and n converges as n tends to infinity.
Implications for the maximal cluster in a finite box are discussed.Comment: 23 pages, 2 figure
Universal properties of knotted polymer rings
By performing Monte Carlo sampling of -steps self-avoiding polygons
embedded on different Bravais lattices we explore the robustness of
universality in the entropic, metric and geometrical properties of knotted
polymer rings. In particular, by simulating polygons with up to we
furnish a sharp estimate of the asymptotic values of the knot probability
ratios and show their independence on the lattice type. This universal feature
was previously suggested although with different estimates of the asymptotic
values. In addition we show that the scaling behavior of the mean squared
radius of gyration of polygons depends on their knot type only through its
correction to scaling. Finally, as a measure of the geometrical
self-entanglement of the SAPs we consider the standard deviation of the writhe
distribution and estimate its power-law behavior in the large limit. The
estimates of the power exponent do depend neither on the lattice nor on the
knot type, strongly supporting an extension of the universality property to
some features of the geometrical entanglement.Comment: submitted to Phys.Rev.
Multigrid Monte Carlo with higher cycles in the Sine Gordon model
We study the dynamical critical behavior of multigrid Monte Carlo for the two
dimensional Sine Gordon model on lattices up to 128 x 128. Using piecewise
constant interpolation, we perform a W-cycle (gamma=2). We examine whether one
can reduce critical slowing down caused by decreasing acceptance rates on large
blocks by doing more work on coarser lattices. To this end, we choose a higher
cycle with gamma = 4. The results clearly demonstrate that critical slowing
down is not reduced in either case.Comment: 7 pages, 1 figure, whole paper including figure contained in ps-file,
DESY 93-00
What is the maximum rate at which entropy of a string can increase?
According to Susskind, a string falling toward a black hole spreads
exponentially over the stretched horizon due to repulsive interactions of the
string bits. In this paper such a string is modeled as a self-avoiding walk and
the string entropy is found. It is shown that the rate at which
information/entropy contained in the string spreads is the maximum rate allowed
by quantum theory. The maximum rate at which the black hole entropy can
increase when a string falls into a black hole is also discussed.Comment: 11 pages, no figures; formulas (18), (20) are corrected (the quantum
constant is added), a point concerning a relation between the Hawking and
Hagedorn temperatures is corrected, conclusions unchanged; accepted by
Physical Review D for publicatio
Self-avoiding walks crossing a square
We study a restricted class of self-avoiding walks (SAW) which start at the
origin (0, 0), end at , and are entirely contained in the square on the square lattice . The number of distinct
walks is known to grow as . We estimate as well as obtaining strict upper and lower bounds,
We give exact results for the number of SAW of
length for and asymptotic results for .
We also consider the model in which a weight or {\em fugacity} is
associated with each step of the walk. This gives rise to a canonical model of
a phase transition. For the average length of a SAW grows as ,
while for it grows as
. Here is the growth constant of unconstrained SAW in . For we provide numerical evidence, but no proof, that the
average walk length grows as .
We also consider Hamiltonian walks under the same restriction. They are known
to grow as on the same lattice. We give
precise estimates for as well as upper and lower bounds, and prove that
Comment: 27 pages, 9 figures. Paper updated and reorganised following
refereein
Efficiency of the Incomplete Enumeration algorithm for Monte-Carlo simulation of linear and branched polymers
We study the efficiency of the incomplete enumeration algorithm for linear
and branched polymers. There is a qualitative difference in the efficiency in
these two cases. The average time to generate an independent sample of
sites for large varies as for linear polymers, but as for branched (undirected and directed) polymers, where
. On the binary tree, our numerical studies for of order
gives . We argue that exactly in this
case.Comment: replaced with published versio
Uncovering the topology of configuration space networks
The configuration space network (CSN) of a dynamical system is an effective
approach to represent the ensemble of configurations sampled during a
simulation and their dynamic connectivity. To elucidate the connection between
the CSN topology and the underlying free-energy landscape governing the system
dynamics and thermodynamics, an analytical soluti on is provided to explain the
heavy tail of the degree distribution, neighbor co nnectivity and clustering
coefficient. This derivation allows to understand the universal CSN network
topology observed in systems ranging from a simple quadratic well to the native
state of the beta3s peptide and a 2D lattice heteropolymer. Moreover CSN are
shown to fall in the general class of complex networks describe d by the
fitness model.Comment: 6 figure
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