Related papers: Approaching the ground states of the random maximu…
A new combinatorial, analytical approach to the ground-state energy problem of spin glasses with different concentrations of +/- J interactions is developed. The energy e_0 is expressed in terms of the fraction of broken bonds mu_0 and…
The scaling of fluctuations in the distribution of ground-state energies or costs with the system size N for Ising spin glasses is considered using an extensive set of simulations with the Extremal Optimization heuristic across a range of…
To provide a novel tool for the investigation of the energy landscape of the Edwards-Anderson spin-glass model we introduce an algorithm that allows an efficient execution of a greedy optimization based on data from a previously performed…
We introduce a method based on semidefinite programming that produces rigorous two-sided bounds on ground state energy densities and correlation functions of translation-invariant classical spin models on infinite lattices. In this method,…
We review several models of glassy systems where the randomness is self generated, i.e. already an infinitesimal amount of disorder is sufficient to cause a transition to a non-ergodic, glassy state. We discuss the application of the…
We describe a numerical study of the potential energy landscape for the two-dimensional XY model (with no disorder), considering up to 100 spins and CPU and GPU implementations of local optimization, focusing on minima and saddles of index…
We examine the ground-state phase diagram of the t-J model in one dimension by means of the Density Matrix Renormalization Group. This model is characterized by a rich phase diagram as a function of the exchange interaction J and the…
With the help of EXACT ground states obtained by a polynomial algorithm we compute the domain wall energy at zero-temperature for the bond-random and the site-random Ising spin glass model in two dimensions. We find that in both models the…
The notion of complex energy landscape underpins the intriguing dynamical behaviors in many complex systems ranging from polymers, to brain activity, to social networks and glass transitions. The spin glass state found in dilute magnetic…
We employ a novel algorithm using a quasi-exact embedded-cluster matching technique as minimization method within a genetic algorithm to reliably obtain numerically exact ground states of the Edwards-Anderson XY spin glass model with…
The complete phase diagram of the Kitaev model with a magnetic field remains elusive, as do the experimental results in the candidate material {\alpha}-RuCl3. Here, we study the Kitaev model on a one-dimensional ladder setting within the…
We establish an asymptotic formula for the ground-state energy of the spherical pure $(p,q)$-spin glass model for $p,q\ge 97$. We achieve this through understanding the concentration of the complexity of critical points with values within a…
We study the 3-spin spherical model with mean-field interactions and Gaussian random couplings. For moderate system sizes of up to 20 spins, we obtain all stationary points of the energy landscape by means of the numerical polynomial…
A novel method for glassy landscape exploration is presented which utilizes a time series of energy values collected during an isothermal relaxation after a thermal quench. A sub-series of increasingly rare events, or quakes, which are…
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…
We study the dynamics of symmetric and asymmetric spin-glass models of size $N$. The analysis is in terms of the double empirical process: this contains both the spins, and the field felt by each spin, at a particular time (without any…
The `lid' algorithm performs an exhaustive exploration of neighborhoods of local energy minima of energy landscapes. This paper describes an implementation of the algorithm, including issues of parallel performance and scalability. To…
The statistics of the ground-state and domain-wall energies for the two-dimensional random-bond Ising model on square lattices with independent, identically distributed bonds of probability $p$ of $J_{ij}= -1$ and $(1-p)$ of $J_{ij}= +1$…
We demonstrate through two case studies, one on the p-spin interaction model and the other on the random K-satisfiability problem, that a heterogeneity transition occurs to the ground-state configuration space of a random…
We present a numerical study of ground states of the dilute versions of the Sherrington-Kirkpatrick (SK) mean-field spin glass. In contrast to so-called "sparse" mean-field spin glasses that have been studied widely on random networks of…