Related papers: Exact solutions for diluted spin glasses and optim…
The quench dynamics of glassy systems are challenging. Due to aging, the system never reaches a stationary state but instead evolves on emergent scales that grow with its age. This slow evolution complicates field-theoretic descriptions, as…
In this paper we generalize to the case of diluted spin models and random combinatorial optimization problems a technique recently introduced by Guerra (cond-mat/0205123) to prove that the replica method generates variational bounds for…
C-dismantling (CD) problem aims at finding the minimum vertex set D of a graph G(V,E) after removing which the remaining graph will break into connected components with the size not larger than C. In this paper, we introduce a spin-glass…
We consider the dynamics of spin facilitated models of glasses in the non-equilibrium aging regime following a sudden quench from high to low temperatures. We briefly review known results obtained for the broad class of kinetically…
We study a simple and exactly solvable model for the generation of random satisfiability problems. These consist of $\gamma N$ random boolean constraints which are to be satisfied simultaneously by $N$ logical variables. In…
The Asymmetric Simple Exclusion Process is one of the most extensively studied models in non-equilibrium statistical mechanics. The macroscopic particle current produced in its steady state is directly related to the breaking of detailed…
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,…
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 consider the critical properties of points of continuous glass transition as one can find in liquids in presence of constraints or in liquids in porous media. Through a one loop analysis we show that the critical Replica Field Theory…
We establish that in the large degree limit, the value of certain optimization problems on sparse random hypergraphs is determined by an appropriate Gaussian optimization problem. This approach was initiated in Dembo et. al.(2016) for…
In the present paper we analyze the critical properties of a quantum spherical spin glass model with short range, random interactions. Since the model allows for rigorous detailed calculations, we can show how the effective partition…
Mean field spin glass models have undergone substantial mathematical development, but finite dimensional short range spin glasses remain much less understood. This paper proves several rigorous zero temperature signatures of glassy behavior…
This thesis includes analysis of disordered spin ensembles corresponding to Exact Cover, a multi-access channel problem, and composite models combining sparse and dense interactions. The satisfiability problem in Exact Cover is addressed…
Across many scientific and engineering disciplines, it is important to consider how much the output of a given system changes due to perturbations of the input. Here, we investigate the glassy phase of $\pm J$ spin glasses at zero…
Spin-glasses are natural Gibbs distributions that have been studied in Theoretical CS for many decades. Recently, they have been gaining attention from the community as they emerge naturally in neural computation and learning, network…
Extremal Optimization (EO), a new local search heuristic, is used to approximate ground states of the mean-field spin glass model introduced by Sherrington and Kirkpatrick. The implementation extends the applicability of EO to systems with…
We study a p-spin spin-glass model to understand if the finite-temperature glass transition found in the mean-field regime of p-spin models, and used to model the behavior of structural glasses, persists in the non-mean-field regime. By…
We include p-spin interactions in a spherical version of a soluble mean-field spin-glass model proposed by van Hemmen. Due to the simplicity of the solutions, which do not require the use of the replica trick, we are able to carry out a…
We consider quantum rotors or Ising spins in a transverse field on a $d$-dimensional lattice, with random, frustrating, short-range, exchange interactions. The quantum dynamics are associated with a finite moment of inertia for the rotors,…
Optimizing a high-dimensional non-convex function is, in general, computationally hard and many problems of this type are hard to solve even approximately. Complexity theory characterizes the optimal approximation ratios achievable in…