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Continuous phase transitions with a convex dip in the microcanonical entropy
Hans Behringer1, Michel Pleimling
1Fakultät für Physik, Universität Bielefeld, D-33615 Bielefeld, Germany.
Summary
A convex dip in microcanonical entropy usually indicates a first-order transition. This study shows such dips in continuous transitions are finite-size effects, not first-order signals.
Area of Science:
- Statistical Mechanics
- Condensed Matter Physics
- Phase Transitions
Background:
- A convex dip in microcanonical entropy typically signals a first-order phase transition.
- However, convex dips have been observed in systems with continuous transitions, like the Baxter-Wu and two-dimensional four-state Potts models.
- The origin of these dips in continuous transitions has remained unclear.
Purpose of the Study:
- To investigate the origin of convex dips in microcanonical entropy for systems exhibiting continuous phase transitions.
- To differentiate these dips from those associated with first-order transitions.
- To develop a theoretical framework for understanding these phenomena in finite systems.
Main Methods:
- Analysis of microcanonical entropy in finite systems.
- Development of a microcanonical finite-size scaling theory for continuous phase transitions.
- Comparison with existing models like the Baxter-Wu and two-dimensional four-state Potts models.
- Numerical simulations to validate theoretical predictions.
Main Results:
- Demonstrated that convex dips in continuous transitions are a result of finite-size effects.
- Characterized the distinct properties of these dips compared to first-order transition signals.
- Validated the microcanonical finite-size scaling theory for continuous phase transitions through numerical simulations.
Conclusions:
- Convex dips in microcanonical entropy for finite systems can arise from finite-size effects in continuous phase transitions.
- These dips do not indicate a first-order transition and possess unique characteristics.
- The proposed finite-size scaling theory provides a robust explanation for these observations.
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