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Critical-point symmetry in a finite system
1Racah Institute of Physics, The Hebrew University, Jerusalem 91904, Israel.
Physical Review Letters
|June 6, 2003
Summary
Finite systems exhibit an effective deformation at second-order phase transition critical points, describing dynamics where intrinsic energy surfaces are typically flat. This effective deformation is found by minimizing energy after symmetry projection, yielding accurate predictions for energies and quadrupole rates.
Area of Science:
- Physics
- Quantum Mechanics
- Statistical Mechanics
Background:
- Second-order phase transitions are characterized by a flat intrinsic energy surface at the critical point.
- Stable minima for deformation are absent at these critical points in the intrinsic frame.
Purpose of the Study:
- To investigate the existence and nature of an effective deformation in finite systems at a second-order phase transition critical point.
- To develop a method for describing the dynamics at the critical point for finite systems.
Main Methods:
- Minimizing the energy surface after projection onto appropriate symmetries to define an effective deformation.
- Deriving analytic expressions for energies and quadrupole rates.
Main Results:
- An effective deformation exists for finite systems at the critical point, capable of describing the system's dynamics.
- Analytic expressions for energies and quadrupole rates were derived.
- These expressions provide good estimates for observables at the critical point.
Conclusions:
- The concept of effective deformation is crucial for understanding the behavior of finite systems at critical points.
- The derived analytic expressions offer a valuable tool for predicting system properties.
- This work provides a new perspective on phase transitions in finite systems.