Related papers: Exploring high-dimensional random landscapes: from…
We study the Langevin dynamics of the standard random heteropolymer model by mapping the problem to a supersymmetric field theory using the Martin-Siggia-Rose formalism. The resulting model is solved non-perturbatively employing a Gaussian…
Given discrete degrees of freedom (spins) on a graph interacting via an energy function, what can be said about the energy local minima and associated inherent structures? Using the lid algorithm in the context of a spin glass energy…
Landscape paradigm is ubiquitous in physics and other natural sciences, but it has to be supplemented with both quantitative and qualitatively meaningful tools for analyzing the topography of a given landscape. We here consider dynamic…
We study the landscapes of multi-species spherical spin glasses. Our results determine the phase boundary for annealed trivialization of the number of critical points, and establish its equivalence with a quenched strong topological…
In the study of disordered models like spin glasses the key object of interest is the rugged energy hypersurface defined in configuration space. The statistical mechanics calculation of the Gibbs-Boltzmann Partition Function gives the…
The complex physics of glass forming systems is controlled by the structure of the low energy portions of their potential energy landscapes. Here, we report that a modified metadynamics algorithm efficiently explores and samples low energy…
We consider the equilibrium dynamics of Ising spin models with multi-spin interactions on sparse random graphs (Bethe lattices). Such models undergo a mean field glass transition upon increasing the graph connectivity or lowering the…
Spin glasses occupy a unique place in condensed matter: they freeze collectively while remaining struc-turally disordered, and they exhibit slow, history-dependent dynamics that reflect an exceptionally rug-ged free-energy landscape. This…
A p-spin interaction Ashkin-Teller spin glass, with three independent Gaussian probability distributions for the exchange interactions, is studied by means of the replica method. A simple phase diagram is obtained within the…
Correlations and other collective phenomena in a schematic model of heterogeneous binary agents (individual spin-glass samples) are considered on the complete graph and also on 2d and 3d regular lattices. The system's stochastic dynamics is…
A complete understanding of the precipitous onset of slow dynamics in systems such as supercooled liquids requires making direct connections between dynamics and the underlying potential energy landscape. With the aid of a switch in…
We present a three-dimensional lattice-gas model with trivial thermodynamics, but nontrivial dynamics. The model is characterized by each particle having its own random energy landscape. The equilibrium dynamics of the model were…
The quantum Ising model with random couplings and random transverse fields on the Cayley tree is studied by Real-Space-Renormalization in order to construct the whole set of eigenstates. The renormalization rules are analyzed via large…
Self-organization through noisy interactions is ubiquitous across physics, mathematics, and machine learning, yet how long-range structure emerges from local noisy dynamics remains poorly understood. Here, we investigate three paradigmatic…
Spin glasses are notoriously difficult to study both analytically and numerically due to the presence of frustration and metastability. Their highly non-convex landscapes require collective updates to explore efficiently. Currently, most…
All ground states and low-lying excitations of a +/- I Ising spin glass model on a cubic 4 x 4 x 4 lattice with periodical boundary conditions were calculated using a method of combinatorical optimization. The structure of states in the…
The equilibrium state of a superfluid in a rotating cylindrical vessel is a vortex crystal -- an array of vortex lines which is stationary in the rotating frame. Experimental realisations of this behaviour typically show a sequence of…
We consider optimization problems for complex systems in which the cost function has a multivalleyed landscape. We introduce a new class of dynamical algorithms which, using a suitable annealing procedure coupled with a balanced…
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…
We study mean field systems whose free energy landscape is dominated by marginally stable states. We review and develop various techniques to describe such states, elucidating their physical meaning and the interrelation between them. In…