Critical dynamical behavior of the Ising model

Liu, Zihua; Vatansever, Erol; Barkema, Gerard T.; Fytas, Nikolaos G.

doi:10.1103/physreve.108.034118

Cited by 3 publications

(1 citation statement)

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“…However, this approach becomes impractical for Ising lattices greater than 4096 2 in the reported specialized hardware, as the 'critical slowing down' problem becomes more severe in larger Ising systems. Recently, [43] found an additional dynamic exponent (z 1 ) in a shorter time scale before the system cross-over to the traditional dynamic exponent of z 2 = 2.167 in single-flip dynamics of Ising models. This means that single-flip algorithms need to overcome not only the diverging autocorrelation time but also this new cross-over effect to obtain high-quality data, which makes such simulations even more difficult.…”

Section: Cluster Algorithm On Parallel Cpusmentioning

confidence: 99%

Critical exponents testing of a random number generator with the Wolff cluster algorithm

Zhu,

Lin,

Sun

et al. 2024

J. Stat. Mech.

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Finite-size scaling (FSS) of critical exponents including γ, β and α of 2D Ising models of sizes up to 327682 are studied using the Wolff clustering algorithm and are used to assess the quality of pseudorandom number generators (PRNGs). Critical exponents of PRNGs with quality issues are found to diverge from their theoretical values at large lattice sizes, similar to previous reports that used the Metropolis algorithm to simulate the Ising lattice. Four high-quality PRNGs, including Mersenne Twister, an additive lagged Fibonacci generator, Xorshift and Xorwow are tested and assessed with their FSS behaviors. Dynamic exponent z is also used to assess the quality of the four tested PRNGs and corroborating results are obtained.

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Section: Cluster Algorithm On Parallel Cpusmentioning

confidence: 99%