Genetic embedded matching approach to ground states in continuous-spin systems

Weigel, Martin

doi:10.1103/physreve.76.066706

Cited by 16 publications

(16 citation statements)

References 77 publications

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“…In real applications one would normally perform runs for many initial conditions and pick the state of lowest energy. This approach is a generic method of improving global optimization algorithms [45,64]. The success probability of a sequence of m runs with different initial conditions follows an exponential,…”

Section: B Comparisons With Ptmentioning

confidence: 99%

Approximate ground states of the random-field Potts model from graph cuts

Kumar

Weigel

et al. 2018

Phys. Rev. E

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While the ground-state problem for the random-field Ising model is polynomial, and can be solved using a number of well-known algorithms for maximum flow or graph cut, the analog random-field Potts model corresponds to a multiterminal flow problem that is known to be NP-hard. Hence an efficient exact algorithm is very unlikely to exist. As we show here, it is nevertheless possible to use an embedding of binary degrees of freedom into the Potts spins in combination with graph-cut methods to solve the corresponding ground-state problem approximately in polynomial time. We benchmark this heuristic algorithm using a set of quasiexact ground states found for small systems from long parallel tempering runs. For a not-too-large number q of Potts states, the method based on graph cuts finds the same solutions in a fraction of the time. We employ the new technique to analyze the breakup length of the random-field Potts model in two dimensions.

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Section: B Comparisons With Ptmentioning

confidence: 99%

Approximate ground states of the random-field Potts model from graph cuts

Kumar

Weigel

et al. 2018

Phys. Rev. E

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“…There are many different ways to construct such a PT protocol and the available freedom in choosing specific details makes their comparison a challenging job [35][36][37][38][39]. Our motivation in the present comparative study is to shed new light on aspects that appear to be still undissolved.…”

Section: Introductionmentioning

confidence: 99%

Comparative study of selected parallel tempering methods

Malakis

Papakonstantinou²

2013

Phys. Rev. E

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We review several parallel tempering schemes and examine their main ingredients for accuracy and efficiency. The present study covers two selection methods of temperatures and several choices for the exchange of replicas, including a recent novel all-pair exchange method. We compare the resulting schemes and measure specific heat errors and efficiency using the two-dimensional (2D) Ising model. Our tests suggest that, an earlier proposal for using numbers of local moves related to the canonical correlation times is one of the key ingredients for increasing efficiency, and protocols using cluster algorithms are found to be very effective. Some of the protocols are also tested for efficiency and ground state production in 3D spin glass models where we find that, a simple nearestneighbor approach using a local n-fold way algorithm is the most effective. Finally, we present evidence that the asymptotic limits of the ground state energy for the isotropic case and that of an anisotropic case of the 3D spin-glass model are very close and may even coincide.

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“…One of the advantages of the chosen code layout is that the total run-times for individual disorder realizations can be chosen independent of each other, thus allowing to accommodate the fat-tailed distribution in "hardness" of disorder realizations to be expected from spin-glass systems [40][41][42]. This flexibility will be essential for performing more extensive simulations of the problem considered here, which will also put to test the reliability of the new compute model in a large-scale application.…”

Section: Discussionmentioning

confidence: 99%

Optimized GPU simulation of continuous-spin glass models

Yavors’kii

Weigel

2012

Eur. Phys. J. Spec. Top.

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Abstract. We develop a highly optimized code for simulating the Edwards-Anderson Heisenberg model on graphics processing units (GPUs). Using a number of computational tricks such as tiling, data compression and appropriate memory layouts, the simulation code combining overrelaxation, heat bath and parallel tempering moves achieves a peak performance of 0.29 ns per spin update on realistic system sizes, corresponding to a more than 150 fold speed-up over a serial CPU reference implementation. The optimized implementation is used to study the spin-glass transition in a random external magnetic field to probe the existence of a de Almeida-Thouless line in the model, for which we give benchmark results.

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Genetic embedded matching approach to ground states in continuous-spin systems

Cited by 16 publications

References 77 publications

Approximate ground states of the random-field Potts model from graph cuts

Approximate ground states of the random-field Potts model from graph cuts

Comparative study of selected parallel tempering methods

Optimized GPU simulation of continuous-spin glass models

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