Ultraviolet-Complete Local Field Theory of Persistent Symmetry Breaking in 2+1 Dimensions
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Summary
This summary is machine-generated.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.
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.
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