Non-reversible Monte Carlo simulations of spin models

Fernandes, Heitor Carpes Marques; Weigel, Martin

doi:10.1016/j.cpc.2010.11.017

Cited by 40 publications

(62 citation statements)

References 7 publications

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“…The Markov chain is characterized by a transition probability w j (σ) per unit time from σ to F j σ. Let p(σ, t) be a probability distribution for finding the spin state σ at time t. Then, the master equation is written as follows: 5) where the first and second terms in the right hand side are outgoing and incoming probability, respectively. For the master equation in Eq.…”

Section: Master Equation and Detailed Balance Conditionmentioning

confidence: 99%

“…Let t ω be a sufficient large integer which ensures equilibrium of the system. Then, the autocorrelation function of the magnetization density is estimated as (4.4) and the integrated autocorrelation time of the magnetization density is 5) where here M is the total number of MCS after t ω steps and the equilibrium values of m eq and m 2 eq are used. Figures 4 and 5 present the numerical results estimated by Eqs.…”

Section: Monte Carlo Simulationsmentioning

confidence: 99%

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Dynamics of One-Dimensional Ising Model without Detailed Balance Condition

Sakai

Hukushima

2013

J. Phys. Soc. Jpn.

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We study an irreversible Markov chain Monte Carlo method based on a skew detailed balance condition for an one-dimensional Ising model. Dynamical behavior of the magnetization density is analyzed in order to understand the properties of this method. As a result, it is found theoretically that the relaxation time of the magnetization density is reduced by using some transition probabilities satisfying the skew detailed balance condition, in comparison to that with the corresponding transition probability with the detailed balance condition, and that one of the transition probabilities changes the dynamical critical exponent even with a local spin update.

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Section: Master Equation and Detailed Balance Conditionmentioning

confidence: 99%

Section: Monte Carlo Simulationsmentioning

confidence: 99%

Dynamics of One-Dimensional Ising Model without Detailed Balance Condition

Sakai

Hukushima

2013

J. Phys. Soc. Jpn.

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“…In addition, ECMC violates detailed balance and only satisfies the weaker global balance condition (cf. [22][23][24][25][26]). Finally, the decision on future moves is based on the change in pair energies, rather than the change in total energy.…”

Section: Introductionmentioning

confidence: 99%

Event-chain Monte Carlo for classical continuous spin models

Michel¹,

Mayer²,

Krauth³

2015

EPL

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We apply the event-chain Monte Carlo algorithm to classical continuum spin models on a lattice and clarify the condition for its validity. In the two-dimensional XY model, it outperforms the local Monte Carlo algorithm by two orders of magnitude, although it remains slower than the Wolff cluster algorithm. In the three-dimensional XY spin glass model at low temperature, the event-chain algorithm is far superior to the other algorithms.

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“…16 The Markov chain lifting framework [17][18][19] unifies these concepts by augmenting the physical configuration space with auxiliary variables that resemble the momentum in Newtonian time evolution and in molecular dynamics (MD). 20 Lifted Markov chains have already been applied to spin models, 23,24 but not to continuum systems.…”

Section: Introductionmentioning

confidence: 99%

Generalized event-chain Monte Carlo: Constructing rejection-free global-balance algorithms from infinitesimal steps

Michel¹,

Kapfer²,

Krauth³

2014

The Journal of Chemical Physics

121

211

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In this article, we present an event-driven algorithm that generalizes the recent hard-sphere event-chain Monte Carlo method without introducing discretizations in time or in space. A factorization of the Metropolis filter and the concept of infinitesimal Monte Carlo moves are used to design a rejection-free Markov-chain Monte Carlo algorithm for particle systems with arbitrary pairwise interactions. The algorithm breaks detailed balance, but satisfies maximal global balance and performs better than the classic, local Metropolis algorithm in large systems. The new algorithm generates a continuum of samples of the stationary probability density. This allows us to compute the pressure and stress tensor as a byproduct of the simulation without any additional computations.

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Non-reversible Monte Carlo simulations of spin models

Cited by 40 publications

References 7 publications

Dynamics of One-Dimensional Ising Model without Detailed Balance Condition

Dynamics of One-Dimensional Ising Model without Detailed Balance Condition

Event-chain Monte Carlo for classical continuous spin models

Generalized event-chain Monte Carlo: Constructing rejection-free global-balance algorithms from infinitesimal steps

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