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Dynamical selection of critical exponents.

Kay Jörg Wiese1

  • 1CNRS-Laboratoire de Physique Théorique de l'Ecole Normale Supérieure, 24 rue Lhomond, 75005 Paris, France and PSL Research University, 62 bis Rue Gay-Lussac, 75005 Paris, France.

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Renormalization group flow typically accesses few fixed points. However, this study reveals a system with infinite fixed points, where dynamics select only one, offering new insights into field theory behavior.

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Area of Science:

  • Theoretical physics
  • Quantum field theory
  • Renormalization group theory

Background:

  • Renormalized field theories usually have few accessible fixed points.
  • Infinite families of fixed points can exist, parameterized by scaling exponents.
  • A nonrenormalizing parameter typically governs these infinite families.

Purpose of the Study:

  • To investigate a novel scenario in field theory with an infinite family of fixed points.
  • To explore the dynamical selection mechanism acting on these fixed points.
  • To understand systems with attractive interactions where the potential vanishes at large fields.

Main Methods:

  • Analysis of fixed-point equations in renormalized field theories.
  • Study of renormalization-group flow dynamics.
  • Investigation of potentials V(ϕ) with specific asymptotic behavior.

Main Results:

  • Identified a scenario with an infinite family of fixed points.
  • Demonstrated that renormalization-group flow dynamically selects a single fixed point from this infinite family.
  • The selection mechanism operates in systems with attractive interactions, similar to ϕ⁴ theory, but with a potential V that vanishes at large ϕ.

Conclusions:

  • The study presents a unique dynamical selection mechanism for fixed points in field theory.
  • This finding expands the understanding of renormalization-group flows and fixed-point structures.
  • The results are relevant for systems with potentials exhibiting attractive interactions and specific large-field behavior, such as defect interactions.