Related papers: Complexity of bipartite spherical spin glasses
In the three-dimensional Heisenberg spin glass in a random field we study the properties of the inherent structures that are obtained by an instantaneous cooling from infinite temperature. For not too large field the density of states…
We investigate the complexity of the Hamiltonian in the pure $p$-spin spin glass model accompanied with a polynomial-type potential on $\mathbb{R}^N$. In this Hamiltonian, the Gaussian field is anisotropic, and the potential lacks…
Recent numerical simulations indicate that several different equilibrium glass transitions may be characterized by diverging correlation lengths, and that these divergences are described by a non-mean-field, Ising-like, critical exponent. I…
We study numerically the properties of local low-energy excitations in the two-dimensional Ising spin glass. Given the ground state, we determine the lowest-lying connected cluster of flipped spins containing one given spin, either with a…
A brief personal perspective is given of issues, questions, formulations, methods, some answers and selected extensions posed by the spin glass problem, showing how considerations of an apparently insignificant and practically unimportant…
We study the classical 1D Heisenberg spin glasses. Based on the Hamilton equations we obtained the system of recurrence equations which allows to perform node-by-node calculations of a spin-chain. It is shown that calculations from first…
In this thesis I discuss combinatorial optimization problems, from the statistical physics perspective. The starting point are the motivations which brought physicists together with computer scientists and mathematicians to work on this…
Recent studies on the spin and the chirality orderings of the three-dimensional Heisenberg spin glass and related systems are reviewed with particular emphasis on the possible spin-chirality decoupling phenomena. Chirality scenario of real…
The pre-asymptotic analysis of the multichannel scattering problem for particles with an arbitrary spin and short-range interactions has been presented. The complete operator-valued dependence of the scattered differential flux on the…
Bethe lattice spins glasses are supposed to be marginally stable, i.e. their equilibrium probability distribution changes discontinuously when we add an external perturbation. So far the problem of a spin glass on a Bethe lattice has been…
The aim of this paper is to review and discuss qualitatively some results on the properties of amorphous packings of hard spheres that were recently obtained by means of the replica method. The theory gives predictions for the equation of…
A spectral minimal partition of a manifold is a decomposition into disjoint open sets that minimizes a spectral energy functional. While it is known that bipartite minimal partitions correspond to nodal partitions of Courant-sharp Laplacian…
There has been a recent surge of powerful tools to show rapid mixing of Markov chains, via functional inequalities such as Poincar\'e inequalities. In many situations, Markov chains fail to mix rapidly from a worst-case initialization, yet…
We discuss the problem of characterizing upper bounds on entanglement in a bipartite quantum system when only the reduced density matrices (marginals) are known. In particular, starting from the known two-qubit case, we propose a family of…
A spin glass is a diluted magnetic material in which the magnetic moments are randomly interacting, with a huge number of metastable states which prevent reaching equilibrium. Spin-glass models are conceptually simple, but require very…
It is a folklore belief in the theory of spin glasses and disordered systems that out-of-equilibrium dynamics fail to find stable local optima exhibiting e.g. local strict convexity on physical time-scales. In the context of the…
We describe the entanglement of two indistinguishable delocalized spin-$\frac{1}{2}$ particles in the simplest spatial configuration of three spatial modes with the constraint that at most one particle occupy each mode. It is show that this…
Marginal optima are minima or maxima of a function with many nearly flat directions. In settings with many competing optima, marginal ones tend to attract algorithms and physical dynamics. Often, the important family of marginal attractors…
Although jammed packings of soft spheres exist in potential energy landscapes with a vast number of minima, when subjected to cyclic shear they may revisit the same configurations repeatedly. Simple hysteretic spin models, in which particle…
The evidently supersymmetric four-dimensional Wess-Zumino model with quenched disorder is considered at the one-loop level. The infrared fixed points of a beta-function form the moduli space $M = RP^2$ where two types of phases were found:…