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O(N)×O(2) scalar models: Including O(∂^{2}) corrections in the functional renormalization group analysis.

Carlos A Sánchez-Villalobos1,2, Bertrand Delamotte2, Nicolás Wschebor3

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This study resolves a 20-year debate on phase transitions in frustrated magnetic systems. It confirms a first-order phase transition for O(N)×O(2) models, aligning with recent conformal bootstrap results.

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Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Quantum Field Theory

Background:

  • Phase transitions in frustrated magnetic systems with O(N)×O(2) symmetry have been controversial for over two decades.
  • Discrepancies exist between theoretical, numerical, and experimental findings, with conflicting predictions of first-order versus second-order transitions.

Purpose of the Study:

  • To revisit and advance functional renormalization group studies of O(N)×O(2) models.
  • To resolve the long-standing controversy regarding the nature of phase transitions in these systems.
  • To investigate the sinusoidal phase of O(N)×O(2) models.

Main Methods:

  • Employing the functional renormalization group (FRG) approach.
  • Extending the derivative expansion of the effective action by including nontrivial second-order derivative terms.
  • Analyzing frustrated magnetic systems with O(N)×O(2) symmetry.

Main Results:

  • Confirmed the first-order nature of the phase transition for physical values of N (N=2, 3).
  • Results align with recent findings from Conformal Bootstrap methods.
  • Qualitatively confirmed earlier perturbative results for the sinusoidal phase.

Conclusions:

  • The study provides a resolution to the 20-year controversy surrounding phase transitions in O(N)×O(2) symmetric frustrated magnetic systems.
  • The findings support the first-order nature of the transition, reconciling theoretical and numerical approaches.
  • Further insights into the sinusoidal phase were obtained.