A cluster Monte Carlo algorithm for 2-dimensional spin glasses

Houdayer, J.

doi:10.1007/pl00011151

Cited by 142 publications

(181 citation statements)

References 18 publications

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“…The latter estimate was qualitatively confirmed by a Monte Carlo renormalizationgroup measurement which indicated η ∼ 0.20 [18] again in what can now be recognized as being the T > T * (L) regime [19]. Later numerical simulation estimates were η ∼ 0.20 [20], η ∼ 0.138 [21], η > 0.20 [22], η = 0.20(2) [7].…”

Section: Introductionmentioning

confidence: 70%

“…The spin interactions J ij were chosen from a bimodal distribution (±1 with equal probability) and from a Gaussian distribution N (0, 1) respectively. During the equilibration phase standard heat-bath updates were combined with the exchange Monte Carlo [17] and the Houdayer cluster method [20] on four replicas. We used 75 temperatures in geometric progression between 0.50 ≤ β ≤ 1.50 and also for 1 ≤ β ≤ 3.…”

Section: Correlation Function Measurementsmentioning

confidence: 99%

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Bimodal Ising spin glass in two dimensions: The anomalous dimension η

Lundow¹,

Campbell²

2018

Phys. Rev. B

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Direct measurements of the spin glass correlation function G(R) for Gaussian and bimodal Ising spin glasses in dimension two have been carried out in the temperature region T ∼ 1. In the Gaussian case the data are consistent with the known anomalous dimension value η ≡ 0. For the bimodal spin glass in this temperature region T > T * (L), well above the crossover T * (L) to the ground state dominated regime, the effective exponent η is clearly non-zero and the data are consistent with the estimate η ∼ 0.28(4) given by McMillan in 1983 from similar measurements. Measurements of the temperature dependence of the Binder cumulant U4(T, L) and the normalized correlation length ξ(T, L)/L for the two models confirms the conclusion that the 2D bimodal model has a non-zero effective η both below and above T * (L). The 2D bimodal and Gaussian interaction distribution Ising spin glasses are not in the same Universality class.

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Section: Introductionmentioning

confidence: 70%

Section: Correlation Function Measurementsmentioning

confidence: 99%

Bimodal Ising spin glass in two dimensions: The anomalous dimension η

Lundow¹,

Campbell²

2018

Phys. Rev. B

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“…The Monte Carlo algorithm that we use also makes use of the CMR representation in addition to parallel tempering and Metropolis sweeps. Similar methods have been previously applied by Swendsen and Wang [17,26,37] and others [38,39,40]. The algorithm is described in more detail in [21], here we provide some additional details about the CMR component of the algorithm.…”

Section: Numerical Methods and Resultsmentioning

confidence: 97%

A Percolation-theoretic Approach to Spin Glass Phase Transitions

Machta

Newman

Stein

2009

Progress in Probability

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The magnetically ordered, low temperature phase of Ising ferro-magnets is manifested within the associated Fortuin-Kasteleyn (FK) random cluster representation by the occurrence of a single positive density percolating cluster. In this paper, we review our recent work on the percolation signature for Ising spin glass ordering -both in the short-range Edwards-Anderson (EA) and infinite-range Sherrington-Kirkpatrick (SK) models -within a two-replica FK representation and also in the different Chayes-Machta-Redner two-replica graphical representation. Numerical studies of the ±J EA model in dimension three and rigorous results for the SK model are consistent in supporting the conclusion that the signature of spin-glass order in these models is the existence of a single percolating cluster of maximal density normally coexisting with a second percolating cluster of lower density.

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“…Las Vegas algorithms are widely used in fields like artificial intelligence [4], biology [5] and others. Monte Carlo algorithms are used in mathematics, condensed matter physics [6]- [8] and others.…”

Section: Introductionmentioning

confidence: 99%

Alternative Coins for Quantum Random Walk Search Optimized for a Hypercube

Tonchev¹

2015

JQIS

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The present paper is focused on non-uniform quantum coins for the quantum random walk search algorithm. This is an alternative to the modification of the shift operator, which divides the search space into two parts. This method changes the quantum coins, while the shift operator remains unchanged and sustains the hypercube topology. The results discussed in this paper are obtained by both theoretical calculations and numerical simulations.

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A cluster Monte Carlo algorithm for 2-dimensional spin glasses

Cited by 142 publications

References 18 publications

Bimodal Ising spin glass in two dimensions: The anomalous dimension η

Bimodal Ising spin glass in two dimensions: The anomalous dimension η

A Percolation-theoretic Approach to Spin Glass Phase Transitions

Alternative Coins for Quantum Random Walk Search Optimized for a Hypercube

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