On infrared divergences in spin glasses

By studying the structure of infrared divergences in a toy propagator in the replica approach to the Ising spin glass below $T_c$, we suggest a possible cancellation mechanism which could decrease the degree of singularity in the loop expansion.Comment: 13 pages, Latex , revised versio

On the structure of correlations in the three dimensional spin glasses

We investigate the low temperature phase of three-dimensional Edwards-Anderson model with Bernoulli random couplings. We show that at a fixed value $Q$ of the overlap the model fulfills the clustering property: the connected correlation functions between two local overlaps decay as a power whose exponent is independent of $Q$ for all $0\le |Q| < q_{EA}$. Our findings are in agreement with the RSB theory and show that the overlap is a good order parameter.Comment: 5 pages, 5 figure

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

Zero-Temperature Limit of the SUSY-breaking Complexity in Diluted Spin-Glass Models

We study the SUSY-breaking complexity of the Bethe Lattice Spin-Glass in the zero temperature limit. We consider both the Gaussian and the bimodal distribution of the coupling constants. For $J_{ij}=\pm 1$ the SUSY breaking theory yields fields distributions that concentrate on integer values at low temperatures, at variance with the unbroken SUSY theory. This concentration takes place both in the quenched as well as in the simpler annealed formulation.Comment: 4 pages, 2 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

Quenched Random Graphs

Spin models on quenched random graphs are related to many important optimization problems. We give a new derivation of their mean-field equations that elucidates the role of the natural order parameter in these models.Comment: 9 pages, report CPTH-A264.109

Generalised Bose-Einstein phase transition in large-mm component spin glasses

It is proposed to understand finite dimensional spin glasses using a $1/m$ expansion, where $m$ is the number of spin components. It is shown that this approach predicts a replica symmetric state in finite dimensions. The point about which the expansion is made, the infinite-$m$ limit, has been studied in the mean-field limit in detail and has a very unusual phase transition, rather similar to a Bose-Einstein phase transition but with $N^{2/5}$ macroscopically occupied low-lying states.Comment: 4 pages (plus a few lines), 3 figures. v2: minor error corrected. v3: numerics supplemented by analytical arguments, references added, figure of density of states adde

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