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Computational Modeling of Retinal Neurons for Visual Prosthesis Research - Fundamental Approaches
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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
PubMed
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.

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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.