1,699 research outputs found
Random RNA under tension
The Laessig-Wiese (LW) field theory for the freezing transition of random RNA
secondary structures is generalized to the situation of an external force. We
find a second-order phase transition at a critical applied force f = f_c. For f
f_c, the extension L as a function of
pulling force f scales as (f-f_c)^(1/gamma-1). The exponent gamma is calculated
in an epsilon-expansion: At 1-loop order gamma = epsilon/2 = 1/2, equivalent to
the disorder-free case. 2-loop results yielding gamma = 0.6 are briefly
mentioned. Using a locking argument, we speculate that this result extends to
the strong-disorder phase.Comment: 6 pages, 10 figures. v2: corrected typos, discussion on locking
argument improve
Lattice Fluid Dynamics from Perfect Discretizations of Continuum Flows
We use renormalization group methods to derive equations of motion for large
scale variables in fluid dynamics. The large scale variables are averages of
the underlying continuum variables over cubic volumes, and naturally live on a
lattice. The resulting lattice dynamics represents a perfect discretization of
continuum physics, i.e. grid artifacts are completely eliminated. Perfect
equations of motion are derived for static, slow flows of incompressible,
viscous fluids. For Hagen-Poiseuille flow in a channel with square cross
section the equations reduce to a perfect discretization of the Poisson
equation for the velocity field with Dirichlet boundary conditions. The perfect
large scale Poisson equation is used in a numerical simulation, and is shown to
represent the continuum flow exactly. For non-square cross sections we use a
numerical iterative procedure to derive flow equations that are approximately
perfect.Comment: 25 pages, tex., using epsfig, minor changes, refernces adde
Interacting crumpled manifolds
In this article we study the effect of a delta-interaction on a polymerized
membrane of arbitrary internal dimension D. Depending on the dimensionality of
membrane and embedding space, different physical scenarios are observed. We
emphasize on the difference of polymers from membranes. For the latter,
non-trivial contributions appear at the 2-loop level. We also exploit a
``massive scheme'' inspired by calculations in fixed dimensions for scalar
field theories. Despite the fact that these calculations are only amenable
numerically, we found that in the limit of D to 2 each diagram can be evaluated
analytically. This property extends in fact to any order in perturbation
theory, allowing for a summation of all orders. This is a novel and quite
surprising result. Finally, an attempt to go beyond D=2 is presented.
Applications to the case of self-avoiding membranes are mentioned
Super-rough phase of the random-phase sine-Gordon model: Two-loop results
We consider the two-dimensional random-phase sine-Gordon and study the
vicinity of its glass transition temperature , in an expansion in small
, where denotes the temperature. We derive
renormalization group equations in cubic order in the anharmonicity, and show
that they contain two universal invariants. Using them we obtain that the
correlation function in the super-rough phase for temperature behaves
at large distances as , where the amplitude
is a universal function of temperature
. This result differs at
two-loop order, i.e., , from the prediction based on
results from the "nearly conformal" field theory of a related fermion model. We
also obtain the correction-to-scaling exponent.Comment: 34 page
Interacting Crumpled Manifolds: Exact Results to all Orders of Perturbation Theory
In this letter, we report progress on the field theory of polymerized
tethered membranes. For the toy-model of a manifold repelled by a single point,
we are able to sum the perturbation expansion in the strength g of the
interaction exactly in the limit of internal dimension D -> 2. This exact
solution is the starting point for an expansion in 2-D, which aims at
connecting to the well studied case of polymers (D=1). We here give results to
order (2-D)^4, where again all orders in g are resummed. This is a first step
towards a more complete solution of the self-avoiding manifold problem, which
might also prove valuable for polymers.Comment: 8 page
2-loop Functional Renormalization for elastic manifolds pinned by disorder in N dimensions
We study elastic manifolds in a N-dimensional random potential using
functional RG. We extend to N>1 our previous construction of a field theory
renormalizable to two loops. For isotropic disorder with O(N) symmetry we
obtain the fixed point and roughness exponent to next order in epsilon=4-d,
where d is the internal dimension of the manifold. Extrapolation to the
directed polymer limit d=1 allows some handle on the strong coupling phase of
the equivalent N-dimensional KPZ growth equation, and eventually suggests an
upper critical dimension of about 2.5.Comment: 4 pages, 3 figure
Loop Model with Generalized Fugacity in Three Dimensions
A statistical model of loops on the three-dimensional lattice is proposed and
is investigated. It is O(n)-type but has loop fugacity that depends on global
three-dimensional shapes of loops in a particular fashion. It is shown that,
despite this non-locality and the dimensionality, a layer-to-layer transfer
matrix can be constructed as a product of local vertex weights for infinitely
many points in the parameter space. Using this transfer matrix, the site
entropy is estimated numerically in the fully packed limit.Comment: 16pages, 4 eps figures, (v2) typos and Table 3 corrected. Refs added,
(v3) an error in an explanation of fig.2 corrected. Refs added. (v4) Changes
in the presentatio
Functional renormalization group at large N for random manifolds
We introduce a method, based on an exact calculation of the effective action
at large N, to bridge the gap between mean field theory and renormalization in
complex systems. We apply it to a d-dimensional manifold in a random potential
for large embedding space dimension N. This yields a functional renormalization
group equation valid for any d, which contains both the O(epsilon=4-d) results
of Balents-Fisher and some of the non-trivial results of the Mezard-Parisi
solution thus shedding light on both. Corrections are computed at order O(1/N).
Applications to the problems of KPZ, random field and mode coupling in glasses
are mentioned
Avalanches in mean-field models and the Barkhausen noise in spin-glasses
We obtain a general formula for the distribution of sizes of "static
avalanches", or shocks, in generic mean-field glasses with
replica-symmetry-breaking saddle points. For the Sherrington-Kirkpatrick (SK)
spin-glass it yields the density rho(S) of the sizes of magnetization jumps S
along the equilibrium magnetization curve at zero temperature. Continuous
replica-symmetry breaking allows for a power-law behavior rho(S) ~ 1/(S)^tau
with exponent tau=1 for SK, related to the criticality (marginal stability) of
the spin-glass phase. All scales of the ultrametric phase space are implicated
in jump events. Similar results are obtained for the sizes S of static jumps of
pinned elastic systems, or of shocks in Burgers turbulence in large dimension.
In all cases with a one-step solution, rho(S) ~ S exp(-A S^2). A simple
interpretation relating droplets to shocks, and a scaling theory for the
equilibrium analog of Barkhausen noise in finite-dimensional spin glasses are
discussed.Comment: 6 pages, 1 figur
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