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Bilal Hawashin1, Junchen Rong2, Michael M Scherer1

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Spontaneous symmetry breaking persists in biconical O(N)×Z_{2} vector models at all temperatures. Discrete symmetry breaking occurs with increasing temperature, respecting the Hohenberg-Mermin-Wagner theorem for N above approximately 15.

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Area of Science:

  • Theoretical Physics
  • Condensed Matter Physics
  • Quantum Field Theory

Background:

  • Spontaneous symmetry breaking is a key concept in physics.
  • Previous studies established such phenomena in specific dimensions or model types (nonlocal or nonunitary).
  • Local ultraviolet-complete theories exhibiting persistent symmetry breaking were not previously established in 2+1 dimensions.

Purpose of the Study:

  • To investigate spontaneous symmetry breaking in local biconical O(N)×Z_{2} vector models in 2+1 dimensions.
  • To analyze the behavior at both zero and finite temperatures.
  • To determine the conditions and critical N for discrete symmetry breaking.

Main Methods:

  • Employing functional methods for analysis.
  • Investigating quantum critical behavior at zero temperature.
  • Calculating the finite-temperature phase diagram.

Main Results:

  • Accurate description of quantum critical behavior for N≥2 at zero temperature.
  • Demonstration of discrete symmetry breaking (O(N)×Z_{2}→O(N)) with increasing temperature for large N.
  • Confirmation that the Hohenberg-Mermin-Wagner theorem is respected, with breaking only in the Z_{2} sector.
  • Determination of a critical N_{c}≈15 for this phenomenon.

Conclusions:

  • Local biconical O(N)×Z_{2} vector models in 2+1 dimensions can exhibit persistent spontaneous symmetry breaking.
  • Discrete symmetry breaking is temperature-dependent and occurs above a critical N.
  • The findings are consistent with fundamental theorems like Hohenberg-Mermin-Wagner.