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We review some recent results on finite dimensional spin glasses by studying recent numerical simulations and their relationship with experiments. In particular we will show results obtained at zero and non zero temperature, focusing in the…
The chapter starts with a historical summary of first attempts to optimize the spin glass Hamiltonian, comparing it to recent results on searching largest cliques in random graphs. Exact algorithms to find ground states in generic spin…
In this study the magnetization phenomenon has been investigated as a behavior of interacting elementary moments ensemble, with the help of Ising model [1] in the frame of non-extensive statistical mechanics. To investigate the physical…
Scaling arguments and precise simulations are used to study the square lattice $\pm J$ Ising spin glass, a prototypical model for glassy systems. Droplet theory predicts, and our numerical results show, entropically-stabilized long range…
A sampling algorithm is presented that generates spin glass configurations of the 2D Edwards-Anderson Ising spin glass at finite temperature, with probabilities proportional to their Boltzmann weights. Such an algorithm overcomes the slow…
We analyse the relationship between dynamics and configuration space structure of Ising spin glass systems. The exact knowledge of the structure of the low--energy landscape is used to study the relaxation of the system by random walk in…
A lattice of locally bistable driven-dissipative cavity polaritons is found theoretically to effectively simulate the Ising model, also enabling an effective transverse field. We benchmark the system performance for spin glass problems, and…
Artificial spin ices are engineered arrays of dipolarly coupled nanobar magnets. They enable direct investigations of fascinating collective phenomena from their diverse microstates. However, experimental access to ground states in the…
We propose a duality analysis for obtaining the critical manifold of two-dimensional spin glasses. Our method is based on the computation of quenched free energies with periodic and twisted periodic boundary conditions on a finite basis.…
A spin glass is a diluted magnetic material in which the magnetic moments are randomly interacting, with a huge number of metastable states which prevent reaching equilibrium. Spin-glass models are conceptually simple, but require very…
Low-temperature spin dynamics can become trapped in long-lived patterns shaped by the geometry of the interaction network. Here we introduce Chladni states: spin configurations obtained by binarizing the eigenmodes of the interaction…
Ising formulations are widely utilized to solve combinatorial optimization problems, and a variety of quantum or semiconductor-based hardware has recently been made available. In combinatorial optimization problems, the existence of local…
We investigate the ground state structure of the three-dimensional Ising spin glass in zero field by determining how the ground state changes in a fixed finite block far from the boundaries when the boundary conditions are changed. We find…
Using Monte Carlo simulations we study cooling-rate effects in a three-dimensional Ising model with four-spin interaction. During coarsening, this model develops growing energy barriers which at low temperature lead to very slow dynamics.…
We propose a new method for exact analytical calculation of the ground-state energy of the Ising spin glass on strips. An outstanding advantage of this method over the numerical transfer matrix technique is that the energy is obtained for…
Population annealing is a Monte Carlo algorithm that marries features from simulated annealing and parallel tempering Monte Carlo. As such, it is ideal to overcome large energy barriers in the free-energy landscape while minimizing a…
The nature of the spin glass state is investigated by studying changes to the ground state when a weak perturbation is applied to the bulk of the system. We consider short range models in three and four dimensions and the infinite range…
We present a large-scale simulation of the three-dimensional Ising spin glass with Gaussian disorder to low temperatures and large sizes using optimized population annealing Monte Carlo. Our primary focus is investigating the number of pure…
We consider the energy difference restricted to a finite volume for certain pairs of incongruent ground states (if they exist) in the d-dimensional Edwards-Anderson (EA) Ising spin glass at zero temperature. We prove that the variance of…
We present a statistical method for complex energy landscape exploration which provides information on the metastable states--or valleys--actually explored by an unperturbed aging process following a quench. Energy fluctuations of record…