Wilson–Polchinski exact renormalization group equation for O (<i>N</i>) systems: leading and next-to-leading orders in the derivative expansion

Bervillier, C.

doi:10.1088/0953-8984/17/20/019

Cited by 19 publications

(19 citation statements)

References 48 publications

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“…[14,24,29,30]. All published results for ν and η to order O(∂ 2 ) have in common that the spurious dependence on remaining unphysical cutoff parameters is monotonous, without displaying local extrema.…”

Section: Jhep07(2005)005mentioning

confidence: 96%

“…Except for N = ∞, there are no published results based on the Polchinski flow for N > 4. However, it has recently been indicated [30] that the results from Polchinski flow and optimised ERG flow also agree for N > 4. In the large N limit, the spread of ν(R) with R is absent, and the results for critical exponents becomes unique, ν(R) = 1, and ω n (R) = 2n − 1, n = 1, 2, .…”

Section: Jhep07(2005)005mentioning

confidence: 98%

“…From a structural point of view, the comparatively strong cutoff dependence beyond leading order is not unexpected and fully in line with the stability considerations detailed in the preceeding section. It remains to be seen whether the next order in the expansion has a stabilising effect on the series [30].…”

Section: Jhep07(2005)005mentioning

confidence: 99%

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Universality and the renormalisation group

Litim

2005

J. High Energy Phys.

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Several functional renormalisation group (RG) equations including Polchinski flows and Exact RG flows are compared from a conceptual point of view and in given truncations. Similarities and differences are highlighted with special emphasis on stability properties. The main observations are worked out at the example of O(N ) symmetric scalar field theories where the flows, universal critical exponents and scaling potentials are compared within a derivative expansion. To leading order, it is established that Polchinski flows and ERG flows -despite their inequivalent derivative expansions -have identical universal content, if the ERG flow is amended by an adequate optimisation. The results are also evaluated in the light of stability and minimum sensitivity considerations. Extensions to higher order and further implications are emphasized.

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Section: Jhep07(2005)005mentioning

confidence: 96%

Section: Jhep07(2005)005mentioning

confidence: 98%

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Universality and the renormalisation group

Litim

2005

J. High Energy Phys.

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“…However progress is still needed in order to get estimates of the exponents which can compete in accuracy with the best methods available [35]. It is possible that the basic differential equations for the effective potential and the coefficients of terms involving derivatives of the fields could be worked backward, at finite ℓ, in order to produce a set of manageable coupled integral equations.…”

Section: Improvement Of the Lpamentioning

confidence: 99%

“…Compared to the improvement of the LPA by the derivative expansion, the improvement of the hierarchical approximation is an underdeveloped subject. On the other hand, it is clear that much progress remains to be done in the ERGE approach in order to match the accuracy of other methods [33,34,23] for the calculation of the critical exponents [35]. We hope that this review will facilitate the communication between the two approaches.…”

Section: Introductionmentioning

confidence: 97%

Nonlinear aspects of the renormalization group flows of Dyson's hierarchical model

Meurice¹

2007

J. Phys. A: Math. Theor.

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Abstract.We review recent results concerning the renormalization group (RG) transformation of Dyson's hierarchical model (HM). This model can be seen as an approximation of a scalar field theory on a lattice. We introduce the HM and show that its large group of symmetry simplifies drastically the blockspinning procedure. Several equivalent forms of the recursion formula are presented with unified notations. Rigorous and numerical results concerning the recursion formula are summarized. It is pointed out that the recursion formula of the HM is inequivalent to both Wilson's approximate recursion formula and Polchinski's equation in the local potential approximation (despite the very small difference with the exponents of the latter). We draw a comparison between the RG of the HM and other RG equations in the local potential approximation. The construction of the linear and nonlinear scaling variables is discussed in an operational way. We describe the calculation of non-universal critical amplitudes in terms of the scaling variables of two fixed points. This question appears as a problem of interpolation between these fixed points. Universal amplitude ratios are calculated. We discuss the large-N limit and the complex singularities of the critical potential calculable in this limit. The interpolation between the HM and more conventional lattice models is presented as a symmetry breaking problem. We briefly introduce models with an approximate supersymmetry. One important goal of this review article is to present a configuration space counterpart, suitable for lattice formulations, of other RG equations formulated in momentum space (sometimes abbreviated as ERGE).

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An Introduction to the Nonperturbative Renormalization Group

Delamotte

2012

Lecture Notes in Physics

311

401

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An elementary introduction to the non-perturbative renormalization group is presented mainly in the context of statistical mechanics. No prior knowledge of field theory is necessary. The aim is this article is not to give an extensive overview of the subject but rather to insist on conceptual aspects and to explain in detail the main technical steps. It should be taken as an introduction to more advanced readings.Comment: 56 page

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Wilson–Polchinski exact renormalization group equation for O (N) systems: leading and next-to-leading orders in the derivative expansion

Cited by 19 publications

References 48 publications

Universality and the renormalisation group

Universality and the renormalisation group

Nonlinear aspects of the renormalization group flows of Dyson's hierarchical model

An Introduction to the Nonperturbative Renormalization Group

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