211 research outputs found
Spin Glass Field Theory with Replica Fourier Transforms
We develop a field theory for spin glasses using Replica Fourier Transforms
(RFT). We present the formalism for the case of replica symmetry and the case
of replica symmetry breaking on an ultrametric tree, with the number of
replicas and the number of replica symmetry breaking steps generic
integers. We show how the RFT applied to the two-replica fields allows to
construct a new basis which block-diagonalizes the four-replica mass-matrix,
into the replicon, anomalous and longitudinal modes. The eigenvalues are given
in terms of the mass RFT and the propagators in the RFT space are obtained by
inversion of the block-diagonal matrix. The formalism allows to express any
-replica vertex in the new RFT basis and hence enables to perform a standard
perturbation expansion. We apply the formalism to calculate the contribution of
the Gaussian fluctuations around the Parisi solution for the free-energy of an
Ising spin glass.Comment: 39 pages, 3 figure
On the hybrid origin of Narcissus biflorus (Amaryllidaceae): analysis of C-banding and rDNA structure
Abstract Giemsa and fluorochrome banding with DAPI and chromomycin A3, were utilized to assess karyological details which correlate N. biflorus with the parental species: N. tazetta and N. poeticus. The banding profile in N. biflorus clearly reproduced the model of its progenitors. The EcoR1 restriction pattern of rDNA obtained by Southern blot hybridization indicated, in our material, that each species has more than one ribosomal gene type and in N. biflorus both the ribosomal repeat units of the progenitor species are present
Statistical mechanics of the random K-SAT model
The Random K-Satisfiability Problem, consisting in verifying the existence of
an assignment of N Boolean variables that satisfy a set of M=alpha N random
logical clauses containing K variables each, is studied using the replica
symmetric framework of diluted disordered systems. We present an exact
iterative scheme for the replica symmetric functional order parameter together
for the different cases of interest K=2, K>= 3 and K>>1. The calculation of the
number of solutions, which allowed us [Phys. Rev. Lett. 76, 3881 (1996)] to
predict a first order jump at the threshold where the Boolean expressions
become unsatisfiable with probability one, is thoroughly displayed. In the case
K=2, the (rigorously known) critical value (alpha=1) of the number of clauses
per Boolean variable is recovered while for K>=3 we show that the system
exhibits a replica symmetry breaking transition. The annealed approximation is
proven to be exact for large K.Comment: 34 pages + 1 table + 8 fig., submitted to Phys. Rev. E, new section
added and references update
Nucleoli, rRNA Genes and ITS Region in Posidonia Oceanica (L.) Delile
The maximum number of nucleoli was counted in interphase nuclei of Posidonia oceanica, and a restriction pattern of nuclear rDNA was obtained after digestion with four restriction endonucleases and Southern hybridization. P. oceanica has only one type of ribosomal gene whose size was estimated to be 18.5 kbp long. The nucleotide sequence of the entire ITS region was also determined by direct sequencing of PCR amplified DNA fragments. The sequence of the ITS region was aligned with those of homologous regions of other monocots available in literature, and phylogenetic trees were obtained
Domain wall propagation and nucleation in a metastable two-level system
We present a dynamical description and analysis of non-equilibrium
transitions in the noisy one-dimensional Ginzburg-Landau equation for an
extensive system based on a weak noise canonical phase space formulation of the
Freidlin-Wentzel or Martin-Siggia-Rose methods. We derive propagating nonlinear
domain wall or soliton solutions of the resulting canonical field equations
with superimposed diffusive modes. The transition pathways are characterized by
the nucleations and subsequent propagation of domain walls. We discuss the
general switching scenario in terms of a dilute gas of propagating domain walls
and evaluate the Arrhenius factor in terms of the associated action. We find
excellent agreement with recent numerical optimization studies.Comment: 28 pages, 16 figures, revtex styl
Viscous Instanton for Burgers' Turbulence
We consider the tails of probability density functions (PDF) for different
characteristics of velocity that satisfies Burgers equation driven by a
large-scale force. The saddle-point approximation is employed in the path
integral so that the calculation of the PDF tails boils down to finding the
special field-force configuration (instanton) that realizes the extremum of
probability. We calculate high moments of the velocity gradient
and find out that they correspond to the PDF with where is the
Reynolds number. That stretched exponential form is valid for negative
with the modulus much larger than its root-mean-square (rms)
value. The respective tail of PDF for negative velocity differences is
steeper than Gaussian, , as well as
single-point velocity PDF . For high
velocity derivatives , the general formula is found:
.Comment: 15 pages, RevTeX 3.
Static chaos and scaling behaviour in the spin-glass phase
We discuss the problem of static chaos in spin glasses. In the case of
magnetic field perturbations, we propose a scaling theory for the spin-glass
phase. Using the mean-field approach we argue that some pure states are
suppressed by the magnetic field and their free energy cost is determined by
the finite-temperature fixed point exponents. In this framework, numerical
results suggest that mean-field chaos exponents are probably exact in finite
dimensions. If we use the droplet approach, numerical results suggest that the
zero-temperature fixed point exponent is very close to
. In both approaches is the lower critical dimension in
agreement with recent numerical simulations.Comment: 28 pages + 6 figures, LateX, figures uuencoded at the end of fil
Classical transverse Ising spin glass with short- range interaction beyond the mean field approximation
The classical transverse field Ising spin- glass model with short-range
interactions is investigated beyond the mean- field approximation for a real d-
dimensional lattice. We use an appropriate nontrivial modification of the
Bethe- Peierls method recently formulated for the Ising spin- glass. The zero-
temperature critical value of the transverse field and the linear
susceptibility in the paramagnetic phase are obtained analytically as functions
of dimensionality d. The phase diagram is also calculated numerically for
different values of d. In the limit d -> infinity, known mean- field results
are consistently reproduced.Comment: LaTex, 11 pages, 2 figure
Localization transition of random copolymers at interfaces
We consider adsorption of random copolymer chains onto an interface within
the model of Garel et al. Europhysics Letters 8, 9 (1989). By using the replica
method the adsorption of the copolymer at the interface is mapped onto the
problem of finding the ground state of a quantum mechanical Hamiltonian. To
study this ground state we introduce a novel variational principle for the
Green's function, which generalizes the well-known Rayleigh-Ritz method of
Quantum Mechanics to nonstationary states. Minimization with an appropriate
trial Green's function enables us to find the phase diagram for the
localization-delocalization transition for an ideal random copolymer at the
interface.Comment: 5 page
Spin glass transition in a magnetic field: a renormalization group study
We study the transition of short range Ising spin glasses in a magnetic
field, within a general replica symmetric field theory, which contains three
masses and eight cubic couplings, that is defined in terms of the fields
representing the replicon, anomalous and longitudinal modes. We discuss the
symmetry of the theory in the limit of replica number n to 0, and consider the
regular case where the longitudinal and anomalous masses remain degenerate.
The spin glass transitions in zero and non-zero field are analyzed in a
common framework. The mean field treatment shows the usual results, that is a
transition in zero field, where all the modes become critical, and a transition
in non-zero field, at the de Almeida-Thouless (AT) line, with only the replicon
mode critical. Renormalization group methods are used to study the critical
behavior, to order epsilon = 6-d. In the general theory we find a stable
fixed-point associated to the spin glass transition in zero field. This
fixed-point becomes unstable in the presence of a small magnetic field, and we
calculate crossover exponents, which we relate to zero-field critical
exponents. In a finite magnetic field, we find no physical stable fixed-point
to describe the AT transition, in agreement with previous results of other
authors.Comment: 36 pages with 4 tables. To be published in Phys. Rev.
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