Related papers: Local excitations in mean field spin glasses
We present a mean field analysis of a fully frustrated Ising spin model on an Ising lattice gas. This is equivalent to a degenerate Blume-Emery-Griffiths model with frustration, which we analyze for different values of the quadrupolar…
We study large-scale, low-energy excitations in the Ising spin glass with Gaussian interactions in two-dimensions at zero temperature, using an optimization algorithm to determine exact ground states. Periodic boundary conditions are…
In the last five decades, mean-field neural-networks have played a crucial role in modelling associative memories and, in particular, the Hopfield model has been extensively studied using tools borrowed from the statistical mechanics of…
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…
We review some recent results on finite dimensional spin glasses by studying recent numerical simulations and their relationship with experiments. In particular we will show results obtained at zero and non zero temperature, focusing in the…
We study the equilibrium properties of an Ising frustrated lattice gas with a mean field replica approach. This model bridges usual {\em Spin Glasses} and a version of {\em Frustrated Percolation} model, and has proven relevant to describe…
In this paper, we investigate the finite connectivity spin-glass problem. Our work is focused on the expansion around the point of infinite connectivity of the free energy of a spin glass on a graph with Poissonian distributed connectivity:…
We study the minimum energy clusters (MEC) above the ground state for the 3-d Edwards-Anderson Ising spin glass in a magnetic field. For fields B below 0.4, we find that the field has almost no effect on the excitations that we can probe,…
The replica method has been used to calculate the interface free energy associated with the change from periodic to anti-periodic boundary conditions in finite-dimensional p-spin glass models in the phase which at mean-field level has…
We investigate the nature of the low-energy, large-scale excitations in the three-dimensional Edwards-Anderson Ising spin glass with Gaussian couplings and free boundary conditions, by studying the response of the ground state to a…
We present a unifying approach to studying the replica symmetric solution in general diluted spin glass models on random $p$-uniform hypergraphs with sparsity parameter $\alpha$. Our result shows that there exist two key regimes in which…
We discuss mean field theory of glasses without quenched disorder focusing on the justification of the replica approach to thermodynamics. We emphasize the assumptions implicit in this method and discuss how they can be verified. The…
We discuss the mean-field theory of spin-glass models with frustrated long-range random spin exchange. We analyze the reasons for breakdown of the simple mean-field theory of Sherrington and Kirkpatrick. We relate the replica-symmetry…
We investigate the properties of the glass phase of a recently introduced spin glass model of soft spins subjected to an anharmonic quartic local potential, which serves as a model of low temperature molecular or soft glasses. We solve the…
We propose a new method for exact analytical calculation of the ground-state energy of the Ising spin glass on strips. An outstanding advantage of this method over the numerical transfer matrix technique is that the energy is obtained for…
We introduce a diluted version of the one dimensional spin-glass model with interactions decaying in probability as an inverse power of the distance. In this model varying the power corresponds to change the dimension in short-range models.…
We present a method to analyze magnetic properties of frustrated Ising spin models on specific hierarchical lattices with random dilution. Disorder is induced by dilution and geometrical frustration rather than randomness in the internal…
Identifying heterogeneous structures in glasses --- such as localized soft spots --- and understanding structure-dynamics relations in these systems remain major scientific challenges. Here we derive an exact expression for the local…
A comprehensive review will be given about the rich mathematical structure of mean field spin glass theory, mostly developed, until now, in the frame of the methods of theoretical physics, based on deep physical intuition and hints coming…
We introduce a Random Energy Model on a hierarchical lattice where the interaction strength between variables is a decreasing function of their mutual hierarchical distance, making it a non-mean field model. Through small coupling series…