Related papers: Hysteretic optimization for the Sherrington-Kirkpa…
The free energy landscape of the Sherrington-Kirkpatrik (SK) Ising spin glass is simple in the framework of the Thouless-Anderson-Palmer (TAP) equations as each solution (which are minima of the free energy) has associated with it a nearby…
The concept of replica symmetry breaking found in the solution of the mean-field Sherrington-Kirkpatrick spin-glass model has been applied to a variety of problems in science ranging from biological to computational and even financial…
A sketch of the chapter appearing under the same heading in the book ``New Optimization Algorithms in Physics'' (A.K. Hartmann and H. Rieger, Eds.) is given. After a general introduction to spin glasses, important aspects of heuristic…
The choice of molecular orbitals is decisive in configuration interaction calculations. In this letter, a democratic description of the ground and excited states follows an orthogonally constrained orbitals optimization to produce…
The Stoner-Wohlfarth is the most used model of magnetic hysteresis, but its computation is time-consuming. We use machine learning to approximate piecewise this model by easy-to-compute analytic functions. Our parametrization is suitable…
Large numbers of ground states of two-dimensional Ising spin glasses with periodic boundary conditions in both directions are calculated for sizes up to 40^2. A combination of a genetic algorithm and Cluster-Exact Approximation is used. For…
Here is proposed a general subgraph-based method for efficiently sampling certain graphical models, typically using subgraphs of a fixed treewidth, and also a related method for finding minimum energy (ground) states. In the case of models…
In simulations of some infinite range spin glass systems with finite connectivity, it is found that for any resonable computational time, the saturatedenergy per spin that is achieved by a cluster algorithm is lowered in comparison to that…
We investigate the properties of S=1/2 Heisenberg clusters with random frustration using exact diagonalizations. This is a model for a quantum spin glass. We show that the average ground state spin is $S \propto \sqrt{N}$, where N is the…
We study hysteresis for a two-dimensional, spin-1/2, nearest-neighbor, kinetic Ising ferromagnet in an oscillating field, using Monte Carlo simulations and analytical theory. Attention is focused on small systems and weak field amplitudes…
The spin-$1$ orthogonal dimer chain is investigated using the Density Matrix Renormalization Group (DMRG) algorithm. A transformation to a basis that uses the local eigenstates of the orthogonal dimers, while retaining the local spin states…
We describe an efficient approximation algorithm for evaluating the ground-state energy of the classical Ising Hamiltonian with linear terms on an arbitrary planar graph. The running time of the algorithm grows linearly with the number of…
In the recent years, considerable attention has been paid to preserving structures and invariants in reduced basis methods, in order to enhance the stability and robustness of the reduced system. In the context of Hamiltonian systems,…
Numerical analysis for the stochastic Stokes equations is still challenging even though it has been well done for the corresponding deterministic equations. In particular, the pre-existing error estimates of finite element methods for the…
We focus on spherical spin glasses whose Parisi distribution has support of the form $[0,q]$. For such models we construct paths from the origin to the sphere which consistently remain close to the ground-state energy on the sphere of…
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…
This article regards numerical optimal control of a class of hybrid systems with hysteresis using solely techniques from nonlinear optimization, without any integer variables. Hysteresis is a rate independent memory effect which often…
Local minima also known as inherent structures are expected to play an essential role for the behavior of spin glasses. Here, we propose techniques to efficiently sample these configurations in Monte Carlo simulations. For the…
We show that it is possible to have hysteretic behavior for magnets that does not form simple closed loops in steady state, but must cycle multiple times before returning to its initial state. We show this by studying the zero-temperature…
The mathematically correct computation of the spin glasses free energy in the infinite range limit crowns 25 years of mathematic efforts in solving this model. The exact solution of the model was found many years ago by using a heuristic…