Critical dynamics of disordered magnets in the three-loop approximation

Прудников, В. В.; Белим, С. В.; Osintsev, E. V.; Fedorenko, Andrei A.

doi:10.1134/1.1130564

Cited by 9 publications

(14 citation statements)

References 9 publications

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“…In [20,22] the universality of z was verified, obtaining z ≈ 2.6, but the leading scaling-correction exponent was not consistent with the static one, as predicted by the FT approach. Moreover, this result is inconsistent with the perturbative FT estimate obtained from analyses of the perturbative expansions [24,25,26,15,27,28,29] at two and three loops, which suggest z ≈ 2. 18.…”

Section: Introductioncontrasting

confidence: 65%

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Relaxational dynamics in 3D randomly diluted Ising models

Hasenbusch

Pelissetto²,

Vicari

2007

J. Stat. Mech.

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Abstract.We study the purely relaxational dynamics (model A) at criticality in threedimensional disordered Ising systems whose static critical behaviour belongs to the randomly diluted Ising universality class. We consider the site-diluted and bonddiluted Ising models, and the ±J Ising model along the paramagnetic-ferromagnetic transition line. We perform Monte Carlo simulations at the critical point using the Metropolis algorithm and study the dynamic behaviour in equilibrium at various values of the disorder parameter. The results provide a robust evidence of the existence of a unique model-A dynamic universality class which describes the relaxational critical dynamics in all considered models. In particular, the analysis of the size-dependence of suitably defined autocorrelation times at the critical point provides the estimate z = 2.35(2) for the universal dynamic critical exponent. We also study the offequilibrium relaxational dynamics following a quench from T = ∞ to T = T c . In agreement with the field-theory scenario, the analysis of the off-equilibrium dynamic critical behavior gives an estimate of z that is perfectly consistent with the equilibrium estimate z = 2.35(2).Relaxational dynamics in 3D randomly diluted Ising models 2

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Section: Introductioncontrasting

confidence: 65%

“…9 we plot z eff (L), defined in (27), and z im (L), defined in (52), versus L To verify that the RBIM at p = 0.55 and the ±J model at p = 0.883 have the same dynamical critical behaviour as the RSIM at p = 0.8, in Fig. 10 we plot the ratio…”

Section: Universality Of Z In the Rbim And ±J Ising Modelmentioning

confidence: 99%

Relaxational dynamics in 3D randomly diluted Ising models

Hasenbusch

Pelissetto²,

Vicari

2007

J. Stat. Mech.

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“…However, the RG expansions are known to be asymptotic at best and resummation is needed to get reliable data on their basis [16]. Further results were obtained by the massive RG approach directly at d = 3 with subsequent resummation of resulting expansions: the two-loop value of the exponent reads z = 2.237 [17], the three-loop one is z = 2.165 [18]. Currently, due to essential technical difficulties, dynamical RG functions of RIM are known only within two-loop accuracy in the minimal subtraction RG scheme and within three loops in the massive RG approach at d = 3.…”

Section: Reviewmentioning

confidence: 99%

“…[5,9,10] and analysed theoretically in Refs. [15,17,18,19,20,8]. In cluster algorithms, as it follows already from their name, the whole clusters of spins are flipped, which gives origin to the non-local dynamics.…”

Section: Reviewmentioning

confidence: 99%

Local and cluster critical dynamics of the 3d random-site Ising model

Ivaneyko

Ilnytskyi

Berche³

et al. 2006

Physica A: Statistical Mechanics and its Applications

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We present the results of Monte Carlo simulations for the critical dynamics of the three-dimensional site-diluted quenched Ising model. Three different dynamics are considered, these correspond to the local update Metropolis scheme as well as to the Swendsen-Wang and Wolff cluster algorithms. The lattice sizes of L=10-96 are analysed by a finite-size-scaling technique. The site dilution concentration p=0.85 was chosen to minimize the correction-to-scaling effects. We calculate numerical values of the dynamical critical exponents for the integrated and exponential autocorrelation times for energy and magnetization. As expected, cluster algorithms are characterized by lower values of dynamical critical exponent than the local one: also in the case of dilution critical slowing down is more pronounced for the Metropolis algorithm. However, the striking feature of our estimates is that they suggest that dilution leads to decrease of the dynamical critical exponent for the cluster algorithms. This phenomenon is quite opposite to the local dynamics, where dilution enhances critical slowing down.Comment: 24 pages, 16 figures, style file include

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“…In recent studies, fiveloop expansions were found and resummed for the twodimensional chiral [97], cubic, and mn models [82]. Finally, summation of three-and four-loop expansions was used to analyze critical dynamics in pure and disordered Ising models [98,99], as well as effects due to long-range interactions [100] and violation of replica symmetry [101].…”

Section: B Z ( )mentioning

confidence: 99%

Divergent perturbation series

Suslov

2005

J. Exp. Theor. Phys.

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-Various perturbation series are factorially divergent. The behavior of their high-order terms can be found by Lipatov's method, according to which they are determined by instanton configurations of appropriate functional integrals. When the Lipatov asymptotics is known and several lowest order terms of the perturbation series are found by direct calculation of diagrams, one can gain insight into the behavior of the remaining terms of the series. Summing it, one can solve (in a certain approximation) various strong-coupling problems. This approach is demonstrated by determining the Gell-Mann-Low functions in ϕ 4 theory, QED, and QCD for arbitrary coupling constants. An overview of the mathematical theory of divergent series is presented, and interpretation of perturbation series is discussed. Explicit derivations of the Lipatov asymptotics are presented for some basic problems in theoretical physics. A solution is proposed to the problem of renormalon contributions, which hampered progress in this field in the late 1970s. Practical perturbation-series summation schemes are described for a coupling constant of order unity and in the strong-coupling limit. An interpretation of the Borel integral is given for "non-Borel-summable" series. High-order corrections to the Lipatov asymptotics are discussed.

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Critical dynamics of disordered magnets in the three-loop approximation

Cited by 9 publications

References 9 publications

Relaxational dynamics in 3D randomly diluted Ising models

Relaxational dynamics in 3D randomly diluted Ising models

Local and cluster critical dynamics of the 3d random-site Ising model

Divergent perturbation series

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