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Criticality versus q in the (2+1)-dimensional Zq clock model
1Department of Physics, Norwegian University of Science and Technology, N-7491 Trondheim, Norway. Joakim.Hove@phys.ntnu.no
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 20, 2003
Summary
The 3D Z(q) clock model reaches its limiting critical behavior by q=5. For q greater than or equal to 5, critical exponents match the infinite-q XY model, indicating early convergence.
Area of Science:
- Statistical mechanics
- Condensed matter physics
Background:
- The Z(q) clock model is a theoretical framework used to study phase transitions.
- Understanding critical phenomena in systems with discrete symmetries is crucial in physics.
Purpose of the Study:
- To investigate the critical properties of the 3D Z(q) clock model.
- To determine the point at which the model's behavior converges to its infinite-q limit.
Main Methods:
- Monte Carlo simulations were employed to study the model.
- Two distinct representations were utilized: the phase representation and the loop-gas/dumbbell-gas representation.
Main Results:
- For q >= 5, the critical exponents alpha (specific heat) and nu (correlation length) were found to match those of the infinite-q limit (XY model).
- This suggests that the limiting behavior of the Z(q) clock model is achieved at relatively small values of q.
Conclusions:
- The 3D Z(q) clock model exhibits a rapid convergence to its critical behavior as q increases.
- The critical properties of the Z(q) clock model for q >= 5 are indistinguishable from the XY model, highlighting the early onset of universality.