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Butera, P.; Comi, M.

doi:10.1103/physreve.55.6391

Cited by 39 publications

(55 citation statements)

References 41 publications

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“…They have been computed within the RG approach, 20,22 by the expansion ( = 4 − d) up to five loops, by the perturbative g expansion at fixed dimension d = 3 up to the same order, by other RG approximations, [23][24][25] by HT expansions, 14,49 and by Monte Carlo methods. 50,51 Our estimates of the first few r + 2n by extended HT expansions are listed in Table X.…”

Section: Asymptotic Scaling and The Equation Of Statementioning

confidence: 99%

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Free energy in a magnetic field and the universal scaling equation of state for the three-dimensional Ising model

Butera

Pernici

2011

Phys. Rev. B

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We have substantially extended the high-temperature and low-magnetic-field (and the related low-temperature and high-magnetic-field) bivariate expansions of the free energy for the conventional three-dimensional Ising model and for a variety of other spin systems generally assumed to belong to the same critical universality class. In particular, we have also derived the analogous expansions for the Ising models with spin s = 1,3/2, . . . and for the lattice Euclidean scalar-field theory with quartic self-interaction, on the simple-cubic and the body-centered-cubic lattices. Our bivariate high-temperature expansions, which extend through 24th order, enable us to compute, through the same order, all higher derivatives of the free energy with respect to the field, namely, all higher susceptibilities. These data make more accurate checks possible, in critical conditions, both of the scaling and the universality properties with respect to the lattice and the interaction structure and also help to improve an approximate parametric representation of the critical equation of state for the three-dimensional Ising model universality class.

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Section: Asymptotic Scaling and The Equation Of Statementioning

confidence: 99%

“…We have estimated the critical values of the HT expansions of the RCCs either directly, by extrapolation 49,62 to K − c of the simple auxiliary function…”

Section: The Ratios R + 2n and The Critical Amplitudes Of The Highmentioning

confidence: 99%

Free energy in a magnetic field and the universal scaling equation of state for the three-dimensional Ising model

Butera

Pernici

2011

Phys. Rev. B

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“…Our derivation of the HT and low-field series, which significantly extend the longest known results, even in zero field [4,[28][29][30][31][32], has been performed for the lattice dimensionalities d = 1,2, . .…”

Section: Introductionmentioning

confidence: 99%

High-temperature expansions of the higher susceptibilities for the Ising model in general dimensiond

Butera¹,

Pernici²

2012

Phys. Rev. E

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The high-temperature expansion coefficients of the ordinary and the higher susceptibilities of the spin-1/2 nearest-neighbor Ising model are calculated exactly up to the 20th order for the general d-dimensional (hyper)simple-cubical lattices. These series are analyzed to study the dependence of critical parameters on the lattice dimensionality. Using the general d expression of the ordinary susceptibility, we have more than doubled the length of the existing series expansion of the critical temperature in powers of 1/d.

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“…Table ?.? contains the results of [3] together with other published estimates of the coefficients of the small z expansion of F (z) coming from high temperature series [50,52,53], simulations [54] and derivative expansion of the Exact RG [55,56]. …”

Section: The Small Field Expansionmentioning

confidence: 99%

Precise determination of critical exponents and equation of state by field theory methods

Zinn-Justin¹

2001

Physics Reports

139

166

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Renormalization group, and in particular its Quantum Field Theory implementation has provided us with essential tools for the description of the phase transitions and critical phenomena beyond mean field theory. We therefore review the methods, based on renormalized φ 4 3 quantum field theory and renormalization group, which have led to a precise determination of critical exponents of the N -vector model [1,2] and of the equation of state of the 3D Ising model [3]. These results are among the most precise available probing field theory in a nonperturbative regime.Precise calculations first require enough terms of the perturbative expansion. However perturbation series are known to be divergent. The divergence has been characterized by relating it to instanton contributions. The information about large order behaviour of perturbation series has then allowed to develop efficient "summation" techniques, based on Borel transformation and conformal mapping [4].We first discuss exponents and describe our recent results [2]. Compared to exponents, the determination of the scaling equation of state of the 3D Ising model involves a few additional (non-trivial) technical steps, like the use of the parametric representation, and the order dependent mapping method. From the knowledge of the equation of state a number of ratio of critical amplitudes can also be derived.Finally we emphasize that few physical quantities which are predicted by renormalization group to be universal have been determined precisely, and much work remains to be done. Considering the steady increase in the available computer Talk given at the Conference "Renormalization Group 2000, Taxco (Mexico), 11-15 Jan. 1999 * Laboratoire de la Direction des Sciences de la Matière du Commissariatà l'Energie Atomique 2 resources, many new calculations will become feasible. In addition to the infinite volume quantities, finite size universal quantities would also be of interest, to provide a more direct contact with numerical simulations. Let us also mention dynamical observables, a largely unexplored territory.

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2n-point renormalized coupling constants in the three-dimensional Ising model:Estimates by high temperature series to orderΒ17

Cited by 39 publications

References 41 publications

Free energy in a magnetic field and the universal scaling equation of state for the three-dimensional Ising model

Free energy in a magnetic field and the universal scaling equation of state for the three-dimensional Ising model

High-temperature expansions of the higher susceptibilities for the Ising model in general dimensiond

Precise determination of critical exponents and equation of state by field theory methods

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