Exact combinatorial algorithms: Ground states of disordered systems

Alava, Mikko J.; Duxbury, Phillip M.; Moukarzel, Cristian F.; Rieger, Heiko

doi:10.1016/s1062-7901(01)80009-4

Cited by 55 publications

(90 citation statements)

References 252 publications

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“…Francesca Colaiori, 1 Mikko J. Alava, 1,2 Gianfranco Durin, 3 Alessandro Magni, 3 The equilibrium and nonequilibrium disorder-induced phase transitions are compared in the randomfield Ising model. We identify in the demagnetized state the correct nonequilibrium hysteretic counterpart of the T 0 ground state, and present evidence of universality.…”

Section: Phase Transitions In a Disordered System In And Out Of Equilmentioning

confidence: 99%

“…These results are of relevance for optimization, and for the generic question of universality in the presence of disorder. Similarities and differences between equilibrium and nonequilibrium states in disordered systems have been widely studied both for their conceptual importance and because the presence of randomness often provides prototypical examples of complex optimization problems [1]. There are also many applications in the physics of materials, where this dichotomy is met, together often with concepts such as aging and glassiness.…”

Section: Phase Transitions In a Disordered System In And Out Of Equilmentioning

confidence: 99%

“…In d 2 there is no phase transition but an effective ferromagnetic regime for small systems. In d 3 the GS displays an equilibrium phase transition induced by the disorder from a low disorder regime where the system is ferromagnetic (FM) to a strong disorder one, where the system is paramagnetic (PM) [1,5]. The equilibrium critical exponents for random-field magnets have been measured experimentally in Fe 0:93 Zn 0:07 F 2 [6,7].…”

Section: Phase Transitions In a Disordered System In And Out Of Equilmentioning

confidence: 99%

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Phase Transitions in a Disordered System in and out of Equilibrium

et al. 2004

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The equilibrium and non-equilibrium disorder induced phase transitions are compared in the random-field Ising model (RFIM). We identify in the demagnetized state (DS) the correct nonequilibrium hysteretic counterpart of the T = 0 ground state (GS), and present evidence of universality. Numerical simulations in d = 3 indicate that exponents and scaling functions coincide, while the location of the critical point differs, as corroborated by exact results for the Bethe lattice. These results are of relevance for optimization, and for the generic question of universality in the presence of disorder.

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Section: Phase Transitions In a Disordered System In And Out Of Equilmentioning

confidence: 99%

Section: Phase Transitions In a Disordered System In And Out Of Equilmentioning

confidence: 99%

Section: Phase Transitions In a Disordered System In And Out Of Equilmentioning

confidence: 99%

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Phase Transitions in a Disordered System in and out of Equilibrium

et al. 2004

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“…The residual energy was calculated as the difference between the obtained approximate energy and the true ground state energy estimated by a wellestablished algorithm [18]. Figure 5 shows the result for J = 2.0 averaged over 80 samples, and Fig.…”

Section: B Resultsmentioning

confidence: 99%

Quantum annealing of the random-field Ising model by transverse ferromagnetic interactions

2007

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We introduce transverse ferromagnetic interactions, in addition to a simple transverse field, to quantum annealing of the random-field Ising model to accelerate convergence toward the target ground state. The conventional approach using only the transverse-field term is known to be plagued by slow convergence when the true ground state has strong ferromagnetic characteristics for the random-field Ising model. The transverse ferromagnetic interactions are shown to improve the performance significantly in such cases. This conclusion is drawn from the analyses of the energy eigenvalues of instantaneous stationary states as well as by the very fast algorithm of Bethe-type mean-field annealing adopted to quantum systems. The present study highlights the importance of a flexible choice of the type of quantum fluctuations to achieve the best possible performance in quantum annealing. The existence of such flexibility is an outstanding advantage of quantum annealing over simulated annealing.

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“…The exact ground state ͑GS͒ calculations are based on the equivalence of the T = 0 RFIM with the maximum flow problem in a graph; 17 we use a polynomial push-relabel preflowtype algorithm. 18,19 If not stated otherwise, we study cubic systems of size L 3 , L ഛ 100.…”

Section: Numerical Resultsmentioning

confidence: 99%

Surface criticality in random field magnets

Laurson

Alava

2005

Phys. Rev. B

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The boundary-induced scaling of three-dimensional random field Ising magnets is investigated close to the bulk critical point by exact combinatorial optimization methods. We measure several exponents describing surface criticality: ␤ 1 for the surface layer magnetization and the surface excess exponents for the magnetization and the specific heat, ␤ s and ␣ s . The latter are related to the bulk phase transition by the same scaling laws as in pure systems, but only with the same violation of the hyperscaling exponent as in the bulk. The boundary disorders faster than the bulk, and the experimental and theoretical implications are discussed.

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Exact combinatorial algorithms: Ground states of disordered systems

Cited by 55 publications

References 252 publications

Phase Transitions in a Disordered System in and out of Equilibrium

Phase Transitions in a Disordered System in and out of Equilibrium

Quantum annealing of the random-field Ising model by transverse ferromagnetic interactions

Surface criticality in random field magnets

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