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Inverse melting and inverse freezing: a spin model
Nurith Schupper1, Nadav M Shnerb
1Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 31, 2005
Summary
Highly degenerate systems can show inverse melting or inverse freezing, where heating causes crystallization or glass transitions, respectively. This study models these phenomena using spin systems and discusses connections to polymer theories.
Area of Science:
- Physics
- Materials Science
- Statistical Mechanics
Background:
- Highly degenerate systems can exhibit unusual phase transitions.
- Inverse melting (crystallization upon heating) and inverse freezing (glass transition upon heating) are rare phenomena.
Purpose of the Study:
- To review and present experimental and theoretical models of inverse melting and freezing.
- To introduce and solve spin models for these phenomena.
- To explore connections to polymer melt theories.
Main Methods:
- Analytical solutions of spin models (Blume-Capel model) using replica trick.
- Perturbative expansion for almost degenerate spin states.
- Review of experimental demonstrations and theoretical models.
Main Results:
- A spin model exhibiting inverse melting was solved analytically.
- A random exchange analogue yielded inverse freezing.
- Qualitative features resemble a class of inverse melting phenomena.
- Connection to Flory-Huggins chi parameter established.
Conclusions:
- Spin models can capture inverse melting and freezing behaviors.
- The phenomenon is linked to entropy and interaction parameters.
- Insights into the microscopic origin and limitations of Flory-Huggins theory are provided.