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 $R$ steps of replica symmetry breaking. For the Parisi limit $R\to\infty$ (continuum replica symmetry breaking) which is relevant for the manifold dimension $D<2$, 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 $M^{\alpha \beta ; \gamma \delta}$, 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 $p$-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