Related papers: Local minima in disordered mean-field ferromagnets
One of the major concerns for neural network training is that the non-convexity of the associated loss functions may cause bad landscape. The recent success of neural networks suggests that their loss landscape is not too bad, but what…
The landscape of low-energy effective field theories stemming from string theory is too vast for a systematic exploration. However, the meadows of the string landscape may be fertile ground for the application of machine learning…
We consider a family of local search algorithms for the minimum-weight spanning tree, indexed by a parameter $\rho$. One step of the local search corresponds to replacing a connected induced subgraph of the current candidate graph whose…
The investigation of magnetic energy landscapes and the search for ground states of magnetic materials using ab initio methods like density functional theory (DFT) is a challenging task. Complex interactions, such as superexchange and…
We study the non-convex optimization landscape for maximum likelihood estimation in the discrete orbit recovery model with Gaussian noise. This model is motivated by applications in molecular microscopy and image processing, where each…
We study the ferromagnetic random field Ising model (RFIM) on a graph $G=(V,E)$ having maximal degree $\Delta$, where the external field at each vertex is an i.i.d. random variable. When the random field distribution is sufficiently…
The spin-1/2 Ising-Heisenberg model on martini and martini-diced lattice is exactly solved using a star-triangle transformation, which affords an exact mapping correspondence to an effective spin-1/2 Ising model on a triangular lattice. The…
In many statistical learning problems, the target functions to be optimized are highly non-convex in various model spaces and thus are difficult to analyze. In this paper, we compute \emph{Energy Landscape Maps} (ELMs) which characterize…
We study numerically the zero temperature Random Field Ising Model on cubic lattices of various linear sizes $ 6 \le L \le 90 $ in three dimensions with the purpose of verifying the validity of universality for disordered systems. For each…
Local search is a powerful heuristic in optimization and computer science, the complexity of which has been studied in the white box and black box models. In the black box model, we are given a graph $G = (V,E)$ and oracle access to a…
Systems with quenched disorder possess complex energy landscapes that are challenging to explore under the conventional Monte Carlo method. In this work, we implement an efficient entropy sampling scheme for accurate computation of the…
We present a new approach to a classical problem in statistical physics: estimating the partition function and other thermodynamic quantities of the ferromagnetic Ising model. Markov chain Monte Carlo methods for this problem have been…
We develop a recently-proposed mapping of the two-dimensional Ising model with random exchange (RBIM), via the transfer matrix, to a network model for a disordered system of non-interacting fermions. The RBIM transforms in this way to a…
We start from the Theory of Random Point Processes to derive n-point coupled master equations describing the continuous dynamics of discrete variables in random graphs. These equations constitute a hierarchical set of approximations that…
We address the issue of universality in two-dimensional disordered Ising systems, by considering long, finite-width strips of ferromagnetic Ising spins with randomly distributed couplings. We calculate the free energy and spin-spin…
We derive four reduced two-dimensional models that describe, at different spatial scales, the micromagnetics of ultrathin ferromagnetic materials of finite spatial extent featuring perpendicular magnetic anisotropy and interfacial…
We present a detailed study of the phase diagram of the Ising model in random graphs with arbitrary degree distribution. By using the replica method we compute exactly the value of the critical temperature and the associated critical…
Recently, we showed that optimization problems, both in infinite as well as in finite dimensions, for continuous variables and soft excluded volume constraints, can display entire isostatic phases where local minima of the cost function are…
Using exact optimization methods, we find all of the ground states of +/- h random-field Ising magnets (RFIM) and of dilute antiferromagnets in a field (DAFF). The degenerate ground states are usually composed of isolated clusters…
We study a two-sublattice Ising metamagnet with nearest and next-nearest-neighbor interactions, in both uniform and random fields. Using a mean-field approximation, we show that the qualitative features of the phase diagrams are…