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Simplest model to study reentrance in physical systems.
Creighton K Thomas1, Helmut G Katzgraber
1Department of Physics and Astronomy, Texas A&M University, College Station, Texas 77843-4242, USA.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 21, 2011
Summary
Reentrant behavior in physical systems is generic when frustration is present. The simplest model shows a ferromagnetic phase at intermediate temperatures, with paramagnetic phases at high and low temperatures.
Area of Science:
- Condensed matter physics
- Statistical mechanics
Background:
- Phase diagrams describe the states of matter under varying conditions.
- Reentrant behavior, where a system transitions into and out of an ordered phase, is a complex phenomenon.
- Understanding reentrance requires studying models with disorder and frustration.
Purpose of the Study:
- To identify the essential conditions for reentrant behavior in physical systems.
- To investigate reentrance in the two-dimensional random-bond Ising model as a fundamental example.
- To determine the role of frustration in enabling reentrant phase diagrams.
Main Methods:
- Numerical investigation of the two-dimensional random-bond Ising model.
- Analysis of both discrete and continuous disorder distributions.
- Mapping the phase diagram in the disorder-temperature plane.
Main Results:
- Reentrant behavior is a generic feature when frustration is present in the model.
- The phase diagram exhibits reentrance for various disorder strengths.
- A paramagnetic phase exists at both high and low temperatures, with a ferromagnetic phase at intermediate temperatures.
Conclusions:
- Frustration is a key ingredient for reentrant behavior in physical systems.
- The two-dimensional random-bond Ising model serves as a simple yet illustrative system for studying reentrance.
- The findings contribute to a deeper understanding of complex phase transitions in disordered systems.
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