High-temperature series for the susceptibility of the spin-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>s</mml:mi></mml:math>Ising model: Analysis of confluent singularities

Camp, William J.; Dyke, J. P. Van

doi:10.1103/physrevb.11.2579

Cited by 143 publications

(45 citation statements)

References 14 publications

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“…Notice that we have freely chosen in equations (9)- (12) between the conventions of Ref. 63 and those of Ref.…”

Section: Assumptions and Aims Of The Series Analysismentioning

confidence: 99%

“…Eq. (9), often called the Wegner expansion 17 , specifies how the dominant scaling behavior, characterized by the universal critical exponent γ and by the critical amplitude C # (S), is modified by analytic and nonanalytic confluent corrections to scaling(CCS) in a close vicinity of the critical point. The leading nonanalytic CCS is characterized by a universal exponent θ and by an amplitude a …”

Section: Assumptions and Aims Of The Series Analysismentioning

confidence: 99%

“…Sykes 7 first pointed out that the exponent γ, which characterizes the divergence of χ, was roughly independent of S and guessed for it a universal "daltonian" value γ = 5/4 . Later on, when longer series [8][9][10] both for the fcc and for other lattices were derived, a weak dependence of the exponents γ and ν on S emerged from the HT analyses, but was soon correctly ascribed to the occurrence of non-analytic "confluent corrections to scaling" (CCS) rather than to a failure of the universality. In those years the existence of CCS had been inferred by various authors both from the numerical analysis of HT series [11][12][13] and from phenomenological fits [14][15][16] to high precision experimental data for some systems close to criticality.…”

Section: Introductionmentioning

confidence: 99%

“…On the fcc lattice, the HT series initially derived through β 12 in Ref. 9 , were later extended in Ref. 21 to order β 14 .…”

Section: Introductionmentioning

confidence: 99%

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Critical universality and hyperscaling revisited for Ising models of general spin using extended high-temperature series

2002

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We have extended through β 23 the high-temperature expansion of the second field derivative of the susceptibility for Ising models of general spin, with nearest-neighbor interactions, on the simple cubic and the body-centered cubic lattices. Moreover the expansions for the nearest-neighbor correlation function, the susceptibility and the second correlation moment have been extended up to β 25 . Taking advantage of these new data, we can improve the accuracy of direct estimates of critical exponents and of hyper-universal combinations of critical amplitudes such as the renormalized fourpoint coupling gr or the quantity usually denoted by R + ξ . In particular, we obtain γ = 1.2371(1), ν = 0.6299(2), γ4 = 4.3647(20), gr = 1.404(3) and R + ξ = 0.2668(5). We have used a variety of series extrapolation procedures and, in some of the analyses, we have assumed that the leading correctionto-scaling exponent θ is universal and roughly known. We have also verified, to high precision, the validity of the hyperscaling relation and of the universality property both with regard to the lattice structure and to the value of the spin.

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“…Notice that we have freely chosen in equations (9)- (12) between the conventions of Ref. 63 and those of Ref.…”

Section: Assumptions and Aims Of The Series Analysismentioning

confidence: 99%

Section: Assumptions and Aims Of The Series Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…On the fcc lattice, the HT series initially derived through β 12 in Ref. 9 , were later extended in Ref. 21 to order β 14 .…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Critical universality and hyperscaling revisited for Ising models of general spin using extended high-temperature series

2002

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“…For systems belonging to the Ising universality class, a large number of experimental studies could be compared with numerical simulations, with the results of series expansion 2 and with field theoretical models 3 . The dynamics of these fluctuating systems where the microscopic elementary process is the atom spin flip exhibits at the transition a "critical slowing down", corresponding to the divergence of ξ, which is much more difficult to experimentally observe.…”

Section: Introductionmentioning

confidence: 99%

Ordering fluctuation dynamics inAuAgZn2

et al. 2015

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The second-order ordering transition of the AuAgZn2 alloy has been studied by coherent x-ray scattering. Within a few degrees above the critical temperature Tc, equilibrium critical fluctuations are observed together with some pre-transitional local ordering connected to sample defects. The speckles observed correspond to heterodyne interference between local ordering and fluctuations and show a mixed static and dynamical behaviour in a narrow domain of a few tenths of degree above Tc. The dynamical behaviour is shown to correspond to the critical slowing down of the fluctuations in the vicinity of the transition (model "A" of Hohenberg and Halperin 1 ). A rough comparison can be carried out with the classical diffusion models. Some improvements of the method are discussed.

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A Theory of Higher‐Order Correlations. II. Generalization to the Ising Model with Arbitrary Spin and to the Blume‐Capel Model

Šamaj

1988

Physica Status Solidi (b)

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High-temperature series for the susceptibility of the spin-sIsing model: Analysis of confluent singularities

Cited by 143 publications

References 14 publications

Critical universality and hyperscaling revisited for Ising models of general spin using extended high-temperature series

Critical universality and hyperscaling revisited for Ising models of general spin using extended high-temperature series

Ordering fluctuation dynamics inAuAgZn2

A Theory of Higher‐Order Correlations. II. Generalization to the Ising Model with Arbitrary Spin and to the Blume‐Capel Model

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