Related papers: On the replica approach to glasses
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…
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…
In this talk I present some of the recent theoretical results that have been obtained on glassy systems like spin glasses or structural glasses. The physical principles at the basis of the theory are explained in a simple language (without…
We consider mean-field vector spin glasses with possibly non-convex interactions. Up to a small perturbation of the parameters defining the model, the asymptotic behavior of the Gibbs measure is described in terms of a critical point of an…
We perform the replica symmetry breaking (RSB) in the vicinity of the point of instability of the replica symmetric solution in the model of axial quadrupolar glass. It is shown that the solution with the first stage RSB is stable against…
The critical behaviour of the dynamical transition of glassy system is controlled by a Replica Symmetric action with n=1 replicas. The most divergent diagrams in the loop expansion correspond at all orders to the solutions of a stochastic…
So far the problem of a spin glass on a Bethe lattice has been solved only at the replica symmetric level, which is wrong in the spin glass phase. Because of some technical difficulties, attempts at deriving a replica symmetry breaking…
A short survey is presented on spin--glass--like states characteristics in complex nonmagnetic systems. We discuss the interplay of the interaction structure and symmetry with the classification scenarios of the replica symmetry breaking.…
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 construct a real space renormalization group (RG) approach for Ising spin glasses on hypercubic lattices within the scheme of the Migdal-Kadanoff approximation using replicas. Our replica symmetric solution yields results consistent with…
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…
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…
It is shown that continuously changing the effective number of interacting particles in p-spin-glass-like model allows to describe the transition from the full replica symmetry breaking glass solution to stable first replica symmetry…
According to the droplet picture of spin glasses, the low-temperature phase of spin glasses should be replica symmetric. However, analysis of the stability of this state suggested that it was unstable and this instability lends support to…
We present a general and powerful numerical method useful to study the density matrix of spin models. We apply the method to finite dimensional spin glasses, and we analyze in detail the four dimensional Edwards-Anderson model with Gaussian…
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 $n$…
Here I will review the theoretical results that have been obtained for spin glasses. I will concentrate my attention on the predictions of the mean field approach in three dimensional systems and on its numerical and experimental…
Some interesting recent advances in the theoretical understanding of neural networks have been informed by results from the physics of disordered many-body systems. Motivated by these findings, this work uses the replica technique to study…
In certain mean field models for spin glasses there occurs a one step replica symmetry breaking pattern. As an example of general $1/N$-corrections in such systems, the fluctuations in the internal energy are calculated. For this specific…
In these notes we introduce briefly the fundamentals of the replica method in the context of liquid theory and the structural glass problem. In particular, we explain and show its usefulness as a computation framework in the context of the…