Related papers: Replica theory for Levy spin glasses
Extensive equilibrium Monte Carlo simulations are performed for a three-dimensional Heisenberg spin glass with the nearest-neighbor Gaussian coupling to investigate its spin-glass and chiral-glass orderings. The occurrence of a…
We revisited, by means of numerical simulations, the one dimensional bond diluted Levy Ising spin glasses outside the limit of validity of mean field theories. In these models the probability that two spins at distance $r$ interact (via a…
Spin-glass systems are universal models for representing many-body phenomena in statistical physics and computer science. High quality solutions of NP-hard combinatorial optimization problems can be encoded into low energy states of…
We discuss interfaces in spin glasses. We present new theoretical results and a numerical method to characterize overlap interfaces and the stability of the spin-glass phase in extended disordered systems. We use this definition to…
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…
We investigate an XY spin-glass model in which both spins and interactions (or couplings) evolve in time, but with widely separated time-scales. For large times this model can be solved using replica theory, requiring two levels of…
We investigate the balanced $M=4$, $p=4$ spin-glass model for a one-dimensional long-range proxy for the finite dimensional short-range $p$-spin glass model to examine the nature of the glass transition beyond mean-field theory. We perform…
We study a variant of the Sherrington-Kirkpatrick (S-K) spin glass model with external field, where the random symmetric couplings matrix does not consist of i.i.d. entries but is instead orthogonally invariant in law. For sufficiently high…
Francesco Guerra and Fabio Toninelli have developped a very powerful technique to study the high temperature behaviour of the Sherrington-Kirkpatrick mean field spin glass model. They show that this model is asymptoticaly comparable to a…
This paper is divided into two parts. The first part concerns several standard scenarios for how short-range spin glasses might behave at low temperature. Earlier theorems of the authors are reviewed, and some new results presented,…
The mean field theory of a spin glass with a specific form of nearest and next nearest neighbor interactions is investigated. Depending on the sign of the interaction matrix chosen we either find the continuous replica symmetry breaking…
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…
The interpolation techniques have become, in the past decades, a powerful approach to lighten several properties of spin glasses within a simple mathematical framework. Intrinsically, for their construction, these schemes were naturally…
We investigate thermodynamic phase transitions of the joint presence of spin glass (SG) and random field (RF) using a random graph model that allows us to deal with the quenched disorder. Therefore, the connectivity becomes a controllable…
We analyze the properties of the energy landscape of {\it finite-size} fully connected p-spin-like models whose high temperature phase is described, in the thermodynamic limit, by the schematic Mode Coupling Theory of super-cooled liquids.…
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…
The study of the mean-field static solution of the Random Blume-Emery-Griffiths-Capel model, an Ising-spin lattice gas with quenched random magnetic interaction, is performed. The model exhibits a paramagnetic phase, described by a stable…
An one-step replica-symmetry-breaking solution for finite connectivity spin-glass models with K body interaction is constructed at finite temperature using the replica method and thermodynamic constraints. In the absence of external fields,…
We study a three-dimensional plaquette spin model whose low temperature dynamics is glassy, due to localised defects and effective kinetic constraints. While the thermodynamics of this system is smooth at all temperatures, we show that…
Multiplex networks consist of a fixed set of nodes connected by several sets of edges which are generated separately and correspond to different networks ("layers"). Here, the Ising model on multiplex networks with two layers is considered,…