579 research outputs found
Stability of the Mezard-Parisi solution for random manifolds
The eigenvalues of the Hessian associated with random manifolds are
constructed for the general case of steps of replica symmetry breaking. For
the Parisi limit (continuum replica symmetry breaking) which is
relevant for the manifold dimension , they are shown to be non negative.Comment: LaTeX, 15 page
Replica Fourier Transforms on Ultrametric Trees, and Block-Diagonalizing Multi-Replica Matrices
The analysis of objects living on ultrametric trees, in particular the
block-diagonalization of 4-replica matrices ,
is shown to be dramatically simplified through the introduction of properly
chosen operations on those objects. These are the Replica Fourier Transforms on
ultrametric trees. Those transformations are defined and used in the present
work.Comment: Latex file, 14 page
Two-particle renormalizations in many-fermion perturbation theory: Importance of the Ward identity
We analyze two-particle renormalizations within many-fermion perturbation
expansion. We show that present diagrammatic theories suffer from lack of a
direct diagrammatic control over the physical two-particle functions. To
rectify this we introduce and prove a Ward identity enabling an explicit
construction of the self-energy from a given two-particle irreducible vertex.
Approximations constructed in this way are causal, obey conservation laws and
offer an explicit diagrammatic control of singularities in dynamical
two-particle functions.Comment: REVTeX4, 4 pages, 2 EPS figure
Spontaneous versus explicit replica symmetry breaking in the theory of disordered systems
We investigate the relation between spontaneous and explicit replica symmetry
breaking in the theory of disordered systems. On general ground, we prove the
equivalence between the replicon operator associated with the stability of the
replica symmetric solution in the standard replica scheme and the operator
signaling a breakdown of the solution with analytic field dependence in a
scheme in which replica symmetry is explicitly broken by applied sources. This
opens the possibility to study, via the recently developed functional
renormalization group, unresolved questions related to spontaneous replica
symmetry breaking and spin-glass behavior in finite-dimensional disordered
systems.Comment: 16 page
An experimental investigation of near critical and supercritical burning of bipropellant droplets
High pressure combustion characteristics of single fuel droplet burning in ai
Finite dimensional corrections to mean field in a short-range p-spin glassy model
In this work we discuss a short range version of the -spin model. The
model is provided with a parameter that allows to control the crossover with
the mean field behaviour. We detect a discrepancy between the perturbative
approach and numerical simulation. We attribute it to non-perturbative effects
due to the finite probability that each particular realization of the disorder
allows for the formation of regions where the system is less frustrated and
locally freezes at a higher temperature.Comment: 18 pages, 5 figures, submitted to Phys Rev
Interaction Flip Identities for non Centered Spin Glasses
We consider spin glass models with non-centered interactions and investigate
the effect, on the random free energies, of flipping the interaction in a
subregion of the entire volume. A fluctuation bound obtained by martingale
methods produces, with the help of integration by parts technique, a family of
polynomial identities involving overlaps and magnetizations
Double Criticality of the Sherrington-Kirkpatrick Model at T=0
Numerical results up to 42nd order of replica symmetry breaking (RSB) are
used to predict the singular structure of the SK spin glass at T=0. We confirm
predominant single parameter scaling and derive corrections for the T=0 order
function q(a), related to a Langevin equation with pseudotime 1/a. a=0 and
a=\infty are shown to be two critical points for \infty-RSB, associated with
two discrete spectra of Parisi block size ratios, attached to a continuous
spectrum. Finite-RSB-size scaling, associated exponents, and T=0-energy are
obtained with unprecedented accuracy.Comment: 4 pages, 5 figure
Interface energies in Ising spin glasses
The replica method has been used to calculate the interface free energy
associated with the change from periodic to anti-periodic boundary conditions
in finite-dimensional spin glasses. At mean-field level the interface free
energy vanishes but after allowing for fluctuation effects, a non-zero
interface free energy is obtained which is significantly different from
numerical expectations.Comment: 4 pages. Minor changes and clarification
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