Related papers: A mechanical approach to mean field spin models
We investigate the classical Renyi entropy S_n and the associated mutual information I_n in the Sherrington-Kirkpatrick (S-K) model, which is the paradigm model of mean-field spin glasses. Using classical Monte Carlo simulations and…
We show that facilitated spin models of cooperative dynamics introduced by Fredrickson and Andersen display on Bethe lattices a glassy behaviour similar to the one predicted by the mode-coupling theory of supercooled liquids and the…
A didactic description of the thermodynamic properties of classical spin systems is given in terms of their quantum counterpart in the Hamiltonian limit. Emphasis is on the construction of the relevant Hamiltonian, and the calculation of…
Mean-field theories of the glass transition predict a phase transition to a dynamically arrested state, yet no such transition is observed in experiments or simulations of finite-dimensional systems. We resolve this long-standing…
In this work we extend the notion of what is meant by a meanfield. Meanfields are approximately maps - through some self consistency relation - of a complex, usually manybody, problem to a simpler more readily solvable problem. This mapping…
We study numerically the three-dimensional $\phi^{4}$ spin glass, a prototypical disordered and discretized Euclidean field theory that manifests inhomogeneities in space and time but considers a homogeneous squared mass and lambda terms.…
We present a unified dynamical mean-field theory for stochastic self-organized critical models. We use a single site approximation and we include the details of different models by using effective parameters and constraints. We identify the…
I present a new method to analyze Glauber dynamics of the Sherrington-Kirkpatrick (SK) spin glass model. The method is based on ideas used in the classical kinetic theory of fluids. I apply it to study spin correlations in the high…
In this letter, we show that the formulae of Bray and Moore for the average logarithm of the number of metastable states in spin glasses can be obtained by calculating the partition function with $m$ coupled replicas with the symmetry among…
connected spin-glass models with a discontinuous transition. In the thermodynamic limit the equilibrium properties in the high temperature phase are described by the schematic Mode Coupling Theory of super-cooled liquids. We show that {\it…
By controlling quantum fluctuations via the Falk-Bruch inequality we give the first rigorous argument for the existence of a spin-glass phase in the quantum Sherrington-Kirkpatrick model with a transverse magnetic field if the temperature…
The mean spherical approximation (MSA) is a closure relation for pair correlation functions (two-point functions) in statistical physics. It can be applied to a wide range of systems, is computationally fairly inexpensive, and when properly…
Lattice molecule models are proposed in order to study statistical mechanics of glass transition in finite dimensions. Molecules in the models are represented by hard Wang tiles and their density is controlled by a chemical potential. An…
A dimer mean-field model for the Ising spin-glass is presented. Despite its simplicity it captures some of the essential features of the spin-glass physics. The distribution of the single-spin magnetization is determined from a…
We discuss a spin glass reminiscent of the Random Energy Model, which allows in particular to recast the Parisi minimization into a more classical Gibbs variational principle, thereby shedding some light on the physical meaning of the order…
Periodic boundary conditions are applied to a ferromagnetic spin lattice. A symmetrical lattice and its contributions all over space are being used. Results, for the Ising model with ferromagnetic interaction that decays as a $1/r^{D+\nu}$…
In many mean-field glassy systems, the low-temperature Gibbs measure is dominated by exponentially many metastable states. We analyze the evolution of the metastable states as temperature changes adiabatically in the solvable case of the…
The study of the normalized sum of random variables and its asymptotic behaviour has been and continues to be a central chapter in probability and statistical mechanics. When those variables are independent the central limit theorem ensures…
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…
This paper studies spin glass to paramagnetic transition in the Spherical Sherrington-Kirkpatrick model with ferromagnetic Curie-Weiss interaction with coupling constant $J$ and inverse temperature $\beta$. The disorder of the system is…