Studying the continuum limit of the Ising model

Kim, Jaekwon; Patrascioiu, Adrian

doi:10.1103/physrevd.47.2588

Cited by 46 publications

(69 citation statements)

References 25 publications

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“…The series on the bcc lattice, for S = 1/2, was extended to the same order only much later 53 and its analysis also confirmed the above conclusion. Further support of these results came also from various more recent MonteCarlo tests [116][117][118][119] . It should be stressed that the finite-order effects are stronger in the calculation of χ 4 (and of the related quantities like g r ) than in the calculation of quantities defined in terms of two-spin correlations, as we have already remarked in Ref.…”

Section: A Comparison With Other Exponent Estimatessupporting

confidence: 56%

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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Section: A Comparison With Other Exponent Estimatessupporting

confidence: 56%

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

2002

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“…To the above values of g (0) c and g c corresponds the values r = 1.5 and r = 1.71. This is in agreement with recent estimates from high-temperature (r = 1.754) [7,8] and strong coupling expansions (r = 1.746) [9] and Monte Carlo simulations (r = 1.71) [10,12]. However the recent RG-improved fifth order perturbative result of Ref.…”

Section: Iterative Proceduressupporting

confidence: 92%

Critical properties of (1+1)-dimensionalφ4theory in light-cone quantization

Salmons¹,

Grangé²,

Werner³

2002

Phys. Rev. D

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The dynamics of the phase transition of the continuum Φ 4 1+1 -theory in Light Cone Quantization is reexamined taking into account fluctuations of the order parameter < Φ > in the form of dynamical zero mode operators (DZMO) which appear in a natural way via the Haag expansion of the field Φ(x) of the interacting theory. The inclusion of the DZM-sector changes significantly the value of the critical coupling, bringing it in agreement within 2% with the most recent Monte-Carlo and high temperature/strong coupling estimates. The critical slowing down of the DZMO governs the low momentum behavior of the dispersion relation through invariance of this DZMO under conformal transformations preserving the local light cone structure. The critical exponent η characterising the scaling behaviour at k 2 → 0 comes out in agreement with the known value 0.25 of the Ising universality class. η is made of two contributions: one, analytic (75%) and another (25%) which can be evaluated only numerically with an estimated error of 3%. The β-function is then found from the non-perturbative expression of the physical mass. It is non-analytic in the coupling constant with a critical exponent ω = 2. However, at D = 2, ω is not parametrisation independent with respect to the space of coupling constants due to this strong non-analytic behaviour.

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“…This is in agreement with recent estimates from high-temperature (r = 1.754) [3,4] and strong coupling expansions (r = 1.746) [5] and Monte Carlo simulations (r = 1.71) [6,7]. A recent high precision estimate [8] …”

Section: Critical Couplingsupporting

confidence: 79%

Dynamical zero modes and criticality in continuous light-cone quantization of Φ1+14

Grangé

Salmons

Werner

2002

Nuclear Physics B - Proceedings Supplements

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Critical behaviour of the 2D scalar field theory in the LC framework is reviewed. The notion of dynamical zero modes is introduced and shown to lead to a non trivial covariant dispersion relation only for Continuous LC Quantization (CLCQ). The critical exponent η is found to be governed by the behaviour of the infinite volume limit under conformal transformations properties preserving the local LC structure. The β-function is calculated exactly and found non-analytic, with a critical exponent ω = 2, in agreement with the conformal field theory prediction of Calabrese et al.

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Studying the continuum limit of the Ising model

Cited by 46 publications

References 25 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

Critical properties of (1+1)-dimensionalφ4theory in light-cone quantization

Dynamical zero modes and criticality in continuous light-cone quantization of Φ1+14

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