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Three-dimensional antiferromagnetic CP(N-1) models.

Francesco Delfino1, Andrea Pelissetto2, Ettore Vicari1

  • 1Dipartimento di Fisica dell'Università di Pisa and INFN, Largo Pontecorvo 3, I-56127 Pisa, Italy.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 13, 2015
PubMed
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The three-dimensional antiferromagnetic CP(N-1) model exhibits a continuous phase transition for N=3, belonging to the O(8) universality class. For N≥4, renormalization-group analysis indicates no stable fixed points for continuous transitions.

Area of Science:

  • Condensed Matter Physics
  • Quantum Field Theory
  • Statistical Mechanics

Background:

  • Antiferromagnetic CP(N-1) models possess global U(N) and local U(1) gauge symmetries.
  • Understanding critical behavior in these models is crucial for statistical mechanics and condensed matter physics.

Purpose of the Study:

  • To investigate the critical behavior of 3D antiferromagnetic CP(N-1) models.
  • To determine the universality class of the three-component ACP(2) model.
  • To analyze the renormalization-group flow for N≥4.

Main Methods:

  • Mapping to a Landau-Ginzburg-Wilson (LGW) model using a staggered gauge-invariant order parameter.
  • Numerical finite-size scaling analysis of ACP(2) and O(8) vector models.
  • Renormalization-group (RG) analysis with perturbative series in two schemes.

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Main Results:

  • The three-component ACP(2) model transitions to the O(8) vector universality class.
  • Numerical results confirm the O(8) universality for ACP(2) and O(8) models.
  • RG analysis for N≥4 reveals no stable fixed points for continuous transitions.

Conclusions:

  • The ACP(2) model shows an enlarged symmetry at its critical point.
  • The study predicts distinct critical behaviors for N=3 versus N≥4.
  • No continuous transitions are found for N≥4 within the analyzed RG framework.