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Renormalization Group Flow Equations and the Phase Transition in O(N)-models

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arxiv hep-ph/0007098 v1 pith:RYALQTYS submitted 2000-07-11 hep-ph nucl-th

classification hep-phnucl-th
keywords betaequationsflowphaserenormalizationtransitionallowcalculated
verification ladder T0 review T1 audit T2 compute T3 formal

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We derive and solve flow equations for a general O(N)-symmetric effective potential including wavefunction renormalization corrections combined with a heat-kernel regularization. We investigate the model at finite temperature and study the nature of the phase transition in detail. Beta functions, fixed points and critical exponents \beta, \nu, \delta and \eta for various N are independently calculated which allow for a verification of universal scaling relations.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. FRG analysis for a relativistic BEC in arbitrary spatial dimensions

    hep-ph 2025-04 conditional novelty 6.0 of 10

    Functional renormalization group flows of a relativistic complex scalar at finite chemical potential confirm that the condensate vanishes for d≤2 in agreement with Mermin-Wagner, while surviving for d>2.

  2. Gravitationally Induced UV Completion of an $O(N)$ Scalar Theory

    hep-th 2026-01 conditional novelty 5.0 of 10

    Gravity's non-minimal coupling drives the quartic self-coupling of an O(N) scalar to zero at an attractive fixed point, making the broken-phase theory UV-complete and bounding the scalar mass.

  3. Proper-time functional renormalization in $O(N)$ scalar models coupled to gravity

    hep-th 2025-08 unverdicted novelty 5.0 of 10

    Proper-time FRG applied to gravity-coupled O(N) scalars largely reproduces scaling solutions and critical properties found with the effective average action, with some quantitative differences at finite and large N de...

  4. A beginner's guide to functional methods in particle physics

    hep-ph 2025-10 accept novelty 1.0 of 10

    A pedagogical review showing how Dyson-Schwinger, 3PI, and Bethe-Salpeter equations can be chained together to compute glueball masses in pure Yang-Mills theory, matching lattice QCD.

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