1,180 research outputs found
Comment on " A simple model for DNA denaturation"
The replacment of mutual avoidance of polymers by a long-range interaction of
the type proposed by Garel etal (Europhys. Lett. 55, 132 (2001),
cond-mat/0101058) is inconsistent with the prevalent renormalization group
arguments.Comment: 2 pages, Comment on Garel etal. Europhys. Lett 55, 132(2001)
cond-mat/0101058. Appeared in Europhys Let
Delocalization transition of the selective interface model: distribution of pseudo-critical temperatures
According to recent progress in the finite size scaling theory of critical
disordered systems, the nature of the phase transition is reflected in the
distribution of pseudo-critical temperatures over the ensemble of
samples of size . In this paper, we apply this analysis to the
delocalization transition of an heteropolymeric chain at a selective
fluid-fluid interface. The width and the shift
are found to decay with the same exponent
, where . The distribution of
pseudo-critical temperatures is clearly asymmetric, and is well
fitted by a generalized Gumbel distribution of parameter . We also
consider the free energy distribution, which can also be fitted by a
generalized Gumbel distribution with a temperature dependent parameter, of
order in the critical region. Finally, the disorder averaged
number of contacts with the interface scales at like with
.Comment: 9 pages,6 figure
Statistics of low energy excitations for the directed polymer in a random medium ()
We consider a directed polymer of length in a random medium of space
dimension . The statistics of low energy excitations as a function of
their size is numerically evaluated. These excitations can be divided into
bulk and boundary excitations, with respective densities
and . We find that both densities follow the scaling
behavior , where is the exponent governing the
energy fluctuations at zero temperature (with the well-known exact value
in one dimension). In the limit , both scaling
functions and behave as , leading to the droplet power law
in the regime . Beyond their common singularity near , the two scaling functions
are very different : whereas decays
monotonically for , the function first decays for
, then grows for , and finally presents a power law
singularity near . The density
of excitations of length accordingly decays as
where
. We obtain , and , suggesting the possible relation
.Comment: 15 pages, 25 figure
Directed polymer in a random medium of dimension 1+1 and 1+3: weights statistics in the low-temperature phase
We consider the low-temperature disorder-dominated phase of the
directed polymer in a random potentiel in dimension 1+1 (where )
and 1+3 (where ). To characterize the localization properties of
the polymer of length , we analyse the statistics of the weights of the last monomer as follows. We numerically compute the probability
distributions of the maximal weight , the probability distribution of the parameter as well as the average values of the higher order
moments . We find that there exists a
temperature such that (i) for , the distributions
and present the characteristic Derrida-Flyvbjerg
singularities at and for . In particular, there
exists a temperature-dependent exponent that governs the main
singularities and as well as the power-law decay of the moments . The exponent grows from the value
up to . (ii) for , the
distribution vanishes at some value , and accordingly the
moments decay exponentially as in . The
histograms of spatial correlations also display Derrida-Flyvbjerg singularities
for . Both below and above , the study of typical and
averaged correlations is in full agreement with the droplet scaling theory.Comment: 13 pages, 29 figure
Glassy phases in Random Heteropolymers with correlated sequences
We develop a new analytic approach for the study of lattice heteropolymers,
and apply it to copolymers with correlated Markovian sequences. According to
our analysis, heteropolymers present three different dense phases depending
upon the temperature, the nature of the monomer interactions, and the sequence
correlations: (i) a liquid phase, (ii) a ``soft glass'' phase, and (iii) a
``frozen glass'' phase. The presence of the new intermediate ``soft glass''
phase is predicted for instance in the case of polyampholytes with sequences
that favor the alternation of monomers.
Our approach is based on the cavity method, a refined Bethe Peierls
approximation adapted to frustrated systems. It amounts to a mean field
treatment in which the nearest neighbor correlations, which are crucial in the
dense phases of heteropolymers, are handled exactly. This approach is powerful
and versatile, it can be improved systematically and generalized to other
polymeric systems
Probing the tails of the ground state energy distribution for the directed polymer in a random medium of dimension via a Monte-Carlo procedure in the disorder
In order to probe with high precision the tails of the ground-state energy
distribution of disordered spin systems, K\"orner, Katzgraber and Hartmann
\cite{Ko_Ka_Ha} have recently proposed an importance-sampling Monte-Carlo
Markov chain in the disorder. In this paper, we combine their Monte-Carlo
procedure in the disorder with exact transfer matrix calculations in each
sample to measure the negative tail of ground state energy distribution
for the directed polymer in a random medium of dimension .
In , we check the validity of the algorithm by a direct comparison with
the exact result, namely the Tracy-Widom distribution. In dimensions and
, we measure the negative tail up to ten standard deviations, which
correspond to probabilities of order . Our results are
in agreement with Zhang's argument, stating that the negative tail exponent
of the asymptotic behavior
as is directly related to the fluctuation exponent
(which governs the fluctuations
of the ground state energy for polymers of length ) via the simple
formula . Along the paper, we comment on the
similarities and differences with spin-glasses.Comment: 13 pages, 16 figure
Protein Folding and Spin Glass
We explicitly show the connection between the protein folding problem and
spin glass transition. This is then used to identify appropriate quantities
that are required to describe the transition. A possible way of observing the
spin glass transition is proposed.Comment: Revtex3+epsf, 8 pages and one postscript figure tarred, compressed
and uuencoded--appended at the end of the file. Minor TeX change
On Heteropolymer Shape Dynamics
We investigate the time evolution of the heteropolymer model introduced by
Iori, Marinari and Parisi to describe some of the features of protein folding
mechanisms. We study how the (folded) shape of the chain evolves in time. We
find that for short times the mean square distance (squared) between chain
configurations evolves according to a power law, . We discuss
the influence of the quenched disorder (represented by the randomness of the
coupling constants in the Lennard-Jones potential) on value of the critical
exponent. We find that decreases from to when
the strength of the quenched disorder increases.Comment: 12 pages, very simple LaTeX file, 6 figures not included, sorry. SCCS
33
Adsorption of a random heteropolymer at a potential well revisited: location of transition point and design of sequences
The adsorption of an ideal heteropolymer loop at a potential point well is
investigated within the frameworks of a standard random matrix theory. On the
basis of semi-analytical/semi-numerical approach the histogram of transition
points for the ensemble of quenched heteropolymer structures with bimodal
symmetric distribution of types of chain's links is constructed. It is shown
that the sequences having the transition points in the tail of the histogram
display the correlations between nearest-neighbor monomers.Comment: 11 pages (revtex), 3 figure
On the multifractal statistics of the local order parameter at random critical points : application to wetting transitions with disorder
Disordered systems present multifractal properties at criticality. In
particular, as discovered by Ludwig (A.W.W. Ludwig, Nucl. Phys. B 330, 639
(1990)) on the case of diluted two-dimensional Potts model, the moments
of the local order parameter scale with a set
of non-trivial exponents . In this paper, we revisit
these ideas to incorporate more recent findings: (i) whenever a multifractal
measure normalized over space occurs in a random
system, it is crucial to distinguish between the typical values and the
disorder averaged values of the generalized moments , since
they may scale with different generalized dimensions and
(ii) as discovered by Wiseman and Domany (S. Wiseman and E. Domany, Phys Rev E
{\bf 52}, 3469 (1995)), the presence of an infinite correlation length induces
a lack of self-averaging at critical points for thermodynamic observables, in
particular for the order parameter. After this general discussion valid for any
random critical point, we apply these ideas to random polymer models that can
be studied numerically for large sizes and good statistics over the samples. We
study the bidimensional wetting or the Poland-Scheraga DNA model with loop
exponent (marginal disorder) and (relevant disorder). Finally,
we argue that the presence of finite Griffiths ordered clusters at criticality
determines the asymptotic value and the minimal value of the typical multifractal spectrum
.Comment: 17 pages, 20 figure
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