Related papers: Replica and Glasses
While in the fully-connected limit the solution of the spin-glass model is known, with the existence of a complex transition on a critical line in the temperature-external field phase diagram, in finite dimensions we don't know if a…
A review of the stochastic stability property for the Gaussian spin glass models is presented and some perspectives discussed.
High-dimensional random landscapes underlie phenomena as diverse as glassy physics and optimization in machine learning, and even their simplest toy models already display extraordinarily rich behavior. This thesis aims to deepen our…
In this thesis I discuss combinatorial optimization problems, from the statistical physics perspective. The starting point are the motivations which brought physicists together with computer scientists and mathematicians to work on this…
Marginal stability is the notion that stability is achieved, but only barely so. This property constrains the ensemble of configurations explored at low temperature in a variety of systems, including spin, electron and structural glasses. A…
The magnetic systems with disorder form an important class of systems, which are under intensive studies, since they reflect real systems. Such a class of systems is the spin glass one, which combines randomness and frustration. The…
We use real replicas to investigate stability of thermodynamic homogeneity of the free energy of the Sherrington-Kirkpatrick (SK) model of spin glasses. Within the replica trick with the replica symmetric ansatz we show that the averaged…
We address the observability problem for ensembles that are described by probability distributions. The problem is to reconstruct a probability distribution of the initial state from the time-evolution of the probability distribution of the…
We discuss replica analytic continuation using several simple models in order to prove mathematically the validity of replica analysis, which is used in a wide range of fields related to large scale complex systems. While replica analysis…
We study critical behaviour of a magnet with cubic anisotropy and quenched scalar disorder which is taken into account by replica method. We derive to first order in $\epsilon$ approximation the renormalization group equations taking into…
This paper discusses the dynamical properties of $p$-spin models with Kac kind interactions. For large but finite interaction range $R$ one finds two different time scales for relaxation. A first relaxation roughly independent of $R$ where…
We study a chain of identical glassy systems in a constrained equilibrium where each bond of the chain is forced to remain at a preassigned distance to the previous one. We apply this description to Mean Field Glassy systems in the limit of…
Systems of globally coupled logistic maps (GCLM) can display complex collective behaviour characterized by the formation of synchronous clusters. In the dynamical clustering regime, such systems possess a large number of coexisting…
A simple model of a frustrated disordered system is presented. Apart from the (very different) physical interpretation, the model shares many features with that of Sherrington-Kirkpatrick for spin glasses, but, as a consequence of its…
The slow non-equilibrium dynamics of the Edwards-Anderson spin glass model on a hierarchical lattice is studied by means of a coarse-grained description based on renormalization concepts. We evaluate the isothermal aging properties and show…
In recent years important progress has been achieved towards proving the validity of the replica predictions for the (asymptotic) mutual information (or "free energy") in Bayesian inference problems. The proof techniques that have emerged…
In spin glass models one can remove minimization of free energy by some order parameter. One can consider hierarchy of order parameters. It is possible to divide energy among these parts. We can consider relaxation process in glass system…
Using an effective potential method, a replica formulism is set up for describing supercooled liquids near their glass transition. The resulting potential is equivalent to that for an Ising spin glass in a magnetic field. Results taken from…
In this talk I will show that usual spin glasses are a peculiar kind of Abelian gauge theory. I will shortly review the techniques used to study them. At the end I will consider more general models (e.g. spin glasses based on non Abelian…
Glass-like materials are nonequilibrium systems where the relaxation time may exceed reasonable time scales of observations. In the present paper a dynamic percolation model is introduced in order to explain the principal properties of…