Related papers: The planted XY model: thermodynamics and inference
A directed graph (digraph) is formed by vertices and arcs (directed edges) from one vertex to another. A feedback vertex set (FVS) is a set of vertices that contains at least one vertex of every directed cycle in this digraph. The directed…
The Parisi formula for the free energy is among the crown jewels in the theory of spin glasses. We present a simpler proof of the lower bound in the case of the spherical mean-field model. Our method follows the TAP approach developed…
We analyze the replica-symmetry-breaking construction in the Sherrington-Kirkpatrick model of a spin glass. We present a general scheme for deriving an exact asymptotic behavior near the critical temperature of the solution with an…
The role of reflection symmetry breaking for the character of the appearance of replica symmetric spin glass state is investigated. We establish the following symmetry rule for classical systems with one order parameter in the replica…
In this paper, we study the low temperature limit of the spherical Crisanti-Sommers variational problem. We identify the $\Gamma$-limit of the Crisanti-Sommers functionals, thereby establishing a rigorous variational problem for the ground…
There are deep analogies between the melting dynamics in systems with a first order phase transition and the dynamics from equilibrium in super-cooled liquids. For a class of Ising spin models undergoing a first order transition - namely…
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 examine the phase diagram of the $p$-interaction spin glass model in a transverse field. We consider a spherical version of the model and compare with results obtained in the Ising case. The analysis of the spherical model, with and…
The directed L-distance minimal dominating set (MDS) problem has wide practical applications in the fields of computer science and communication networks. Here, we study this problem from the perspective of purely theoretical interest. We…
We determine the structure of the Parisi measure at zero temperature for the spherical p+s spin glass model. We show that depending on the values of p and s, four scenarios may emerge, including the existence of 1-FRSB and 2-FRSB phases as…
We study a 7-state Potts glass model in three dimensions with first, second, and third neighbor interactions with a bimodal distribution of couplings by Monte Carlo simulations. Our results show the existence of a spin-glass transition at a…
In this talk I will review the approach to spin glasses based on the spontaneously broken replica symmetry. I will concentrate my attention mostly on more general ideas, skipping technical details and stressing the characteristic…
Using numerical self-consistent solutions of a sequence of finite replica symmetry breakings (RSB) and Wilson's renormalization group but with the number of RSB-steps playing a role of decimation scales, we report evidence for a non-trivial…
We analyse a linear regression problem with nonconvex regularization called smoothly clipped absolute deviation (SCAD) under an overcomplete Gaussian basis for Gaussian random data. We propose an approximate message passing (AMP) algorithm…
The effect of correlations in disorder variables is a largely unexplored topic in spin glass theory. We study this problem through a specific example of correlated disorder introduced in the Ising spin glass model. We prove that the…
We report progress in understanding the fermionic Ising spin glass with arbitrary filling. A crossover from a magnetically disordered single band phase via two intermediate bands just below the freezing temperature to a 3-band structure at…
We propose a duality analysis for obtaining the critical manifold of two-dimensional spin glasses. Our method is based on the computation of quenched free energies with periodic and twisted periodic boundary conditions on a finite basis.…
We study the competition between ferromagnetic and spin glass phases using a system of coupled infinite-range Ising and Sherrington-Kirkpatrick models. We obtain the replica-symmetric solution for the free energy of this system in terms of…
Purpose of this paper is to face up to P-spin glass and Gaussian P-spin model, i.e. spin glasses with polynomial interactions of degree P > 2. We consider the replica symmetry and first step of replica simmetry breaking assumptions and we…
We consider the problem of predicting the spin states in a kinetic Ising model when spin trajectories are observed for only a finite fraction of sites. In a Bayesian setting, where the probabilistic model of the spin dynamics is assumed to…