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.
769-795
Jüttner, Andreas
a90ff7c5-ae8f-4c8e-9679-b5a95b2a6247
Litim, Daniel F.
de725e0c-5101-4868-8f67-d3d5867ccaa2
Marchais, Edouard
34f2e3dd-95ec-4408-a012-00ee31e9d97d
1 August 2017
Jüttner, Andreas
a90ff7c5-ae8f-4c8e-9679-b5a95b2a6247
Litim, Daniel F.
de725e0c-5101-4868-8f67-d3d5867ccaa2
Marchais, Edouard
34f2e3dd-95ec-4408-a012-00ee31e9d97d
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: http://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: 16 Mar 2024 03:40
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Author:
Daniel F. Litim
Author:
Edouard Marchais
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