Related papers: Ultrametric Broken Replica Symmetry RaMOSt
Diluted mean-field models are spin systems whose geometry of interactions is induced by a sparse random graph or hypergraph. Such models play an eminent role in the statistical mechanics of disordered systems as well as in combinatorics and…
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 $n$…
We investigate stability of replica symmetry breaking solutions in generalized $p$-spin models. It is shown that the kind of the transition to the one-step replica symmetry breaking state depends not only on the presence or absence of the…
We introduce the concept of Random Multi-Overlap Structures in diluted spin glasses, following the ideas of Aizenman, Sims and Starr for non-diluted models. As a result, we prove the generalized bound and variational principle for the free…
Here we review the approach to glassy systems based on the replica method and we introduce the main ingredients of replica symmetry breaking. We explain why the replica method has been successful in spin glass and why it should be…
In this talk I will review the approach to spin glasses based on the spontaneously broken replica symmetry. I will concentrate my attention mostly on more general ideas, skipping technical details and stressing the characteristic…
The analysis of the solution with full replica symmetry breaking in the vicinity of $T_c$ of a general spin glass model with reflection symmetry is performed. The leading term in the order parameter function expansion is obtained. Parisi…
By numerical simulations of the $3d$ Ising spin glass we find evidence that spontaneous replica symmetry breaking theory and not the droplet model describes with good accuracy the equilibrium behavior of the system.
We introduce a mathematical framework based on simple combinatorial arguments (Kernel Representation) that allows to deal successfully with spin glass problems, among others. Let $\Omega^{N}$ be the space of configurations of an $N-$ spins…
This is a short review about recent methods and results, mostly for mean field spin glasses, based on interpolation and comparison schemes. In particular, the Parisi spontaneous replica symmetry breaking phenomenon is described in the frame…
We introduce a new parameter to investigate replica symmetry breaking transitions using finite-size scaling methods. Based on exact equalities initially derived by F. Guerra this parameter is a direct check of the self-averaging character…
Random Overlap Structures (ROSt's) are random elements on the space of probability measures on the unit ball of a Hilbert space, where two measures are identified if they differ by an isometry. In spin glasses, they arise as natural limits…
In this chapter we report on the measurements of the overlap distribution of the replica symmetry breaking solution in complex disordered systems. After a general introduction to the problem of the experimental validation of the Parisi…
We apply the cavity method to a spin glass model on a `small world' lattice, a random bond graph super-imposed upon a 1-dimensional ferromagnetic ring. We show the correspondence with a replicated transfer matrix approach, up to the level…
We consider a system composed by N atoms trapped within a multimode cavity, whose theoretical description is captured by a disordered multimode Dicke model. We show that in the resonant, zero field limit the system exactly realizes the…
The role of reflection symmetry breaking for the character of the appearance of replica symmetric spin glass state is investigated. We establish the following symmetry rule for classical systems with one order parameter in the replica…
A longstanding open question in the theory of disordered systems is whether short-range models, such as the random field Ising model or the Edwards-Anderson model, can indeed have the famous properties that characterize mean-field spin…
In this thesis, we review and examine the replica method from several viewpoints. The replica method is a mathematical technique to calculate general moments of stochastic variables. This method provides a systematic way to evaluate…
We propose a method for calculating the Franz-Parisi potential for spin glass models on sparse random graphs using the replica method under the replica symmetric ansatz. The resulting self-consistent equations have the solution with the…
We explore the consequences of Replica Symmetry Breaking at zero temperature. We introduce a repulsive coupling between a system and its unperturbed ground state. In the Replica Symmetry Breaking scenario a finite coupling induces a non…