Event-chain Monte Carlo for classical continuous spin models

Michel, Manon; Mayer, Johannes; Krauth, Werner

doi:10.1209/0295-5075/112/20003

Cited by 39 publications

(67 citation statements)

References 34 publications

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“…In particle systems with periodic boundary conditions, for example, atoms may continue to move preferentially in certain directions. In continuous spin systems, likewise, configurations realize the equilibrium distribution even though spins rotate in a preferred way [7][8][9] . ECMC moves (displacements of particles, rotations of spins, etc.)…”

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confidence: 99%

All-atom computations with irreversible Markov chains

Faulkner

Qin

Maggs

et al. 2018

The Journal of Chemical Physics

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We apply the irreversible event-chain Monte Carlo (ECMC) algorithm to the simulation of dense all-atom systems with long-range Coulomb interactions. ECMC is event-driven and exactly samples the Boltzmann distribution. It neither uses time-step approximations nor spatial cutoffs on the range of the interaction potentials. Most importantly, it need not evaluate the total Coulomb potential and thus circumvents the major computational bottleneck of traditional approaches. It only requires the derivatives of the two-particle Coulomb potential, for which we discuss mutually consistent choices. ECMC breaks up the total interaction potential into factors. For particle systems made up of neutral dipolar molecules, we demonstrate the superior performance of dipole-dipole factors that do not decompose the Coulomb potential beyond the two-molecule level. We demonstrate that these long-range factors can nevertheless lead to local lifting schemes, where subsequently moved particles are mostly close to each other. For the simple point-charge water model with flexible molecules (SPC/Fw), which combines the long-ranged intermolecular Coulomb potential with hydrogen-oxygen bond-length vibrations, a flexible hydrogen-oxygen-hydrogen bond angle, and Lennard-Jones oxygen-oxygen potentials, we break up the potential into factors containing between two and six particles. For this all-atom liquid-water model, we demonstrate that the computational complexity of ECMC scales very well with the system size. This is achieved in a pure particle-particle framework, without the interpolating mesh required for the efficient implementation of other modern Coulomb algorithms. Finally, we discuss prospects and challenges for ECMC and outline several future applications.

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confidence: 99%

All-atom computations with irreversible Markov chains

Faulkner

Qin

Maggs

et al. 2018

The Journal of Chemical Physics

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“…We illustrate the generality of the clock method by discussing its application in the EC method for the O(n) spin model with n ≥ 2. [32,33]. With an auxiliary lifting variable j that specifies the moving spin, the EC method proposes to rotate infinitesimally its angle as φ j → φ j +dφ.…”

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confidence: 99%

Clock Monte Carlo methods

2019

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We propose the clock Monte Carlo technique for sampling each successive chain step in constant time. It is built on a recently proposed factorized transition filter and its core features include its O(1) computational complexity and its generality. We elaborate how it leads to the clock factorized Metropolis (clock FMet) method, and discuss its application in other update schemes. By grouping interaction terms into boxes of tunable sizes, we further formulate a variant of the clock FMet algorithm, with the limiting case of a single box reducing to the standard Metropolis method. A theoretical analysis shows that an overall acceleration of O(N κ ) (0 ≤ κ ≤ 1) can be achieved compared to the Metropolis method, where N is the system size and the κ value depends on the nature of the energy extensivity. As a systematic test, we simulate long-range O(n) spin models in a wide parameter regime: for n = 1, 2, 3, with disordered algebraically decaying or oscillatory Ruderman-Kittel-Kasuya-Yoshida-type interactions and with and without external fields, and in spatial dimensions from d = 1, 2, 3 to mean-field. The O(1) computational complexity is demonstrated, and the expected acceleration is confirmed. Its flexibility and its independence from the interaction range guarantee that the clock method would find decisive applications in systems with many interaction terms.

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“…We applied the event-chain Monte Carlo algorithm [1][2][3][4] to asymptotically free models in two dimensions. In the literature, these models are considered as toy models of lattice QCD that allow for testing of algorithmic and theoretical ideas in a simplified setting.…”

Section: Discussionmentioning

confidence: 99%

Testing the event-chain algorithm in asymptotically free models

Hasenbusch

Schaefer

2018

Phys. Rev. D

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We apply the event-chain algorithm proposed by Bernard, Krauth and Wilson in 2009 to toy models of lattice QCD. We give a formal prove of stability of the algorithm. We study its performance at the example of the massive Gaussian model on the square and the simple cubic lattice, the O(3)-invariant non-linear σ-model and the SU (3) × SU (3) principle chiral model on the square lattice.In all these cases we find that critical slowing down is essentially eliminated.

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Event-chain Monte Carlo for classical continuous spin models

Cited by 39 publications

References 34 publications

All-atom computations with irreversible Markov chains

All-atom computations with irreversible Markov chains

Clock Monte Carlo methods

Testing the event-chain algorithm in asymptotically free models

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