Related papers: Optimizing glassy p-spin models
Spin Glasses (SG) are paradigmatic models for physical, computer science, biological and social systems. The problem of studying the dynamics for SG models is NP hard, i.e., no algorithm solves it in polynomial time. Here we implement the…
High-dimensional random landscapes underlie phenomena as diverse as glassy physics and optimization in machine learning, and even their simplest toy models already display extraordinarily rich behavior. This thesis aims to deepen our…
In this work, the computational complexity of a spin-glass three-dimensional (3D) Ising model (for the lattice size N = lmn, where l, m, n are the numbers of lattice points along three crystallographic directions) is studied. We prove that…
A patchwork method is used to study the dynamics of loss and recovery of an initial configuration in spin glass models in dimensions d=1 and d=2. The patchwork heuristic is used to accelerate the dynamics to investigate how models might…
We examine the phase diagram of the $p$-interaction spin glass model in a transverse field. We consider a spherical version of the model and compare with results obtained in the Ising case. The analysis of the spherical model, with and…
We present the detailed analysis of the spherical s+p spin glass model with two competing interactions: among p spins and among s spins. The most interesting case is the 2+p model with p > 3 for which a very rich phase diagram occurs,…
A promising paradigm of quantum computing for achieving practical quantum advantages is quantum annealing or quantum approximate optimization algorithm, where the classical problems are encoded in Ising interactions. However, it is…
In these lectures I will present an introduction to the modern way of studying the properties of glassy systems. I will start from soluble models of increasing complications, the Random Energy Model, the $p$-spins interacting model and I…
Finding the ground states of the Ising Hamiltonian [1] maps to various combinatorial optimization problems in biology, medicine, wireless communications, artificial intelligence, and social network. So far no efficient classical and quantum…
The Ising spin glass in two dimensions exhibits rich behavior with subtle differences in the scaling for different coupling distributions. We use recently developed mappings to graph-theoretic problems together with highly efficient…
This study focuses on the problem of finding ground states of random instances of the Sherrington-Kirkpatrick (SK) spin-glass model with Gaussian couplings. While the ground states of SK spin-glass instances can be obtained with branch and…
A method is presented, which allows to sample directly low-temperature configurations of glassy systems, like spin glasses. The basic idea is to generate ground states and low lying excited configurations using a heuristic algorithm. Then,…
We present an algorithm for the optimization and thermal equilibration of spin glasses - or more generally, cost functions of the Ising form $H=\sum_{\langle i j\rangle} J_{ij} s_i s_j + \sum_i h_i s_i$, defined on graphs with arbitrary…
Brief review is given on recent numerical research of the ordering of two typical models of spin glasses (SGs), the three-dimensional (3D) Ising SG and the 3D Heisenberg SG models. Particular attention is paid to the questions of whether…
In this work we study numerically a short range p-spin glass model in three dimensions. The behaviour of the model appears to be remarkably different from mean field predictions. In fact it shares some features typical of models with full…
Counting the number of ground states for a spin-glass or NP-complete combinatorial optimization problem is even more difficult than the already hard task of finding a single ground state. In this paper the entropy of minimum vertex-covers…
We introduce a Hamiltonian for two interacting $su(2)$ spins. We use a mean-field analysis and exact Bethe ansatz results to investigate the ground-state properties of the system in the classical limit, defined as the limit of infinite spin…
We study the large $N$-dimensional limit of the Hessian spectrum at the global minimum of some subclasses of the spherical mixed $p$-spin models. Specifically, we show that its empirical spectral measure converges in probability to a…
Photonic Ising Machines constitute an emergent new paradigm of computation, geared towards tackling combinatorial optimization problems that can be reduced to the problem of finding the ground state of an Ising model. Spatial Photonic Ising…
A new approach known as flat histogram method is used to study the +/-J Ising spin glass in two dimensions. Temperature dependence of the energy, the entropy, and other physical quantities can be easily calculated and we give the results…