Critical exponents of the dilute Ising model from four-loop expansions

Mayer, Imke

doi:10.1088/0305-4470/22/14/028

Cited by 90 publications

(92 citation statements)

References 20 publications

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“…The 2D RDI critical behavior has been also investigated by using this field-theoretical approach and the so-called replica trick. The analysis of the corresponding five-loop perturbative expansions 7,34 gives results which are substantially consistent with the marginal irrelevance of disorder.…”

Section: Renormalization-group Flow and Finite-size Scalingsupporting

confidence: 67%

Universal dependence on disorder of two-dimensional randomly diluted and random-bond±JIsing models

Hasenbusch

Toldin

Pelissetto³

et al. 2008

Phys. Rev. E

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We consider the two-dimensional randomly site diluted Ising model and the random-bond ±J Ising model (also called Edwards-Anderson model), and study their critical behavior at the paramagnetic-ferromagnetic transition. The critical behavior of thermodynamic quantities can be derived from a set of renormalization-group equations, in which disorder is a marginally irrelevant perturbation at the two-dimensional Ising fixed point. We discuss their solutions, focusing in particular on the universality of the logarithmic corrections arising from the presence of disorder.Then, we present a finite-size scaling analysis of high-statistics Monte Carlo simulations. The numerical results confirm the renormalization-group predictions, and in particular the universality of the logarithmic corrections to the Ising behavior due to quenched dilution.

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Section: Renormalization-group Flow and Finite-size Scalingsupporting

confidence: 67%

Universal dependence on disorder of two-dimensional randomly diluted and random-bond±JIsing models

Hasenbusch

Toldin

Pelissetto³

et al. 2008

Phys. Rev. E

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“…Overall, there is a disparity in the exponents reported for that model between results obtained using field-theoretic techniques 31,32 and between those of simulation and experiment. [33][34][35]29 Field-theoretic values 32,31 for the exponent ␥ are larger than that for the pure Ising model (␥ Bulk ϭ1.239Ϯ0.001), ranging from 1.321 to 1.335. Simulation results and experimental values suggest an exponent that is even larger, with reported values varying from 1.3 to 1.5.…”

Section: B Numerical Results For the Critical Temperature And Exponentsmentioning

confidence: 88%

Equilibrium phase transitions in a porous medium

1996

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Static critical phenomena of a three-dimensional Ising model confined in a porous medium made by spinodal decomposition have been studied using large-scale Monte Carlo simulations. We thus examine the influence of the geometry of Vycor-like materials on phase transitions. No surface interactions ͑preference of the Vycor-like material for one phase above the other͒ are taken into account. We find that the critical temperature depends on the average pore size D as T c (D)ϭT c (ϱ)Ϫc/D. The critical exponents are independent of pore size: we find ϭ0.8Ϯ0.1, ␥ϭ1.4Ϯ0.1, ␤ϭ0.65Ϯ0.13. No divergence is observed for the specific heat, indicating ␣р0. All data for all pore sizes can be collapsed well with the scaling function for the magnetic susceptibility L Ϫ␥/ ϭ˜(tL 1/ ), where tϭT/T c (D)Ϫ1. These critical phenomena are consistent with those computed for the randomly site-diluted Ising model. Experimental realizations of our numerical experiments are discussed.

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“…This can be shown by using the standard replica trick to average over the random impurity field [83]. The expansion coefficients and sums of renormalization-group series were calculated for these systems in the four-, five-, and six-loop approximations in [69,84], [85], and [86,87], respectively (see also [88,89]). …”

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 exponents of the dilute Ising model from four-loop expansions

Cited by 90 publications

References 20 publications

Universal dependence on disorder of two-dimensional randomly diluted and random-bond±JIsing models

Universal dependence on disorder of two-dimensional randomly diluted and random-bond±JIsing models

Equilibrium phase transitions in a porous medium

Divergent perturbation series

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