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Global Wilson–Fisher fixed points

Global Wilson–Fisher fixed points
Global Wilson–Fisher fixed points
The Wilson–Fisher fixed point with O(N) universality in three dimensions is studied using the renormalisation group. It is shown how a combination of analytical and numerical techniques determine global fixed points to leading order in the derivative expansion for real or purely imaginary fields with moderate numerical effort. Universal and non-universal quantities such as scaling exponents and mass ratios are computed, for all N , together with local fixed point coordinates, radii of convergence, and parameters which control the asymptotic behaviour of the effective action. We also explain when and why finite- N results do not converge pointwise towards the exact infinite- N limit. In the regime of purely imaginary fields, a new link between singularities of fixed point effective actions and singularities of their counterparts by Polchinski are established. Implications for other theories are indicated.
0550-3213
769-795
Jüttner, Andreas
a90ff7c5-ae8f-4c8e-9679-b5a95b2a6247
Litim, Daniel F.
de725e0c-5101-4868-8f67-d3d5867ccaa2
Marchais, Edouard
34f2e3dd-95ec-4408-a012-00ee31e9d97d
Jüttner, Andreas
a90ff7c5-ae8f-4c8e-9679-b5a95b2a6247
Litim, Daniel F.
de725e0c-5101-4868-8f67-d3d5867ccaa2
Marchais, Edouard
34f2e3dd-95ec-4408-a012-00ee31e9d97d

Jüttner, Andreas, Litim, Daniel F. and Marchais, Edouard (2017) Global Wilson–Fisher fixed points. Nuclear Physics B, 921, 769-795. (doi:10.1016/j.nuclphysb.2017.06.010).

Record type: Article

Abstract

The Wilson–Fisher fixed point with O(N) universality in three dimensions is studied using the renormalisation group. It is shown how a combination of analytical and numerical techniques determine global fixed points to leading order in the derivative expansion for real or purely imaginary fields with moderate numerical effort. Universal and non-universal quantities such as scaling exponents and mass ratios are computed, for all N , together with local fixed point coordinates, radii of convergence, and parameters which control the asymptotic behaviour of the effective action. We also explain when and why finite- N results do not converge pointwise towards the exact infinite- N limit. In the regime of purely imaginary fields, a new link between singularities of fixed point effective actions and singularities of their counterparts by Polchinski are established. Implications for other theories are indicated.

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Accepted/In Press date: 12 June 2017
Published date: 1 August 2017

Identifiers

Local EPrints ID: 412563
URI: https://eprints.soton.ac.uk/id/eprint/412563
ISSN: 0550-3213
PURE UUID: 332bf8e2-a840-4e93-8bb9-5c3565250096

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Date deposited: 21 Jul 2017 16:31
Last modified: 14 Aug 2019 17:25

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