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Three-dimensional ferromagnetic CP^{N-1} models.

Andrea Pelissetto1, Ettore Vicari2

  • 1Dipartimento di Fisica dell'Università di Roma Sapienza and INFN Sezione di Roma I, I-00185 Roma, Italy.

Physical Review. E
|October 3, 2019
PubMed
Summary
This summary is machine-generated.

We studied ferromagnetic CP^{N-1} models using numerical simulations. For N=2, a second-order transition was found, while N=3 and N=4 showed first-order transitions, challenging standard theories.

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Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Quantum Field Theory

Background:

  • Ferromagnetic CP^{N-1} models exhibit global U(N) and local U(1) symmetries.
  • Understanding critical phenomena in these models is crucial for theoretical physics.

Purpose of the Study:

  • Investigate the critical behavior of 3D ferromagnetic CP^{N-1} models for N=2, 3, and 4.
  • Determine the universality classes and transition orders.
  • Analyze the large-N limit and compare with the Landau-Ginzburg-Wilson framework.

Main Methods:

  • Numerical simulations of lattice models for N=2, 3, and 4.
  • Analysis of critical transitions and universality classes.
  • Large-N limit calculations for lattice Hamiltonians.

Main Results:

  • N=2 exhibits a critical transition in the Heisenberg O(3) universality class.
  • N=3 and N=4 show first-order transitions, with N=3's being weak and observable for L≳50.
  • Large-N limit confirms a stable CP^{N-1} fixed point.

Conclusions:

  • The study contradicts the standard Landau-Ginzburg-Wilson prediction of generic first-order transitions for N≥3.
  • Numerical findings highlight the complex critical behavior of these models, deviating from conventional theoretical expectations.