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Random energy model in nonextensive statistical mechanics.

D B Saakian1, E E Vogel

  • 1Yerevan Physics Institute, Alikhanian Brothers St. 2, Yerevan 375036, Armenia.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 3, 2001
PubMed
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Researchers explored the random energy model using nonextensive statistical mechanics. The system

Area of Science:

  • Statistical mechanics
  • Condensed matter physics

Background:

  • The random energy model (REM) is a fundamental model in statistical physics used to study disordered systems.
  • Nonextensive statistical mechanics provides a framework for analyzing systems with long-range interactions or memory effects, characterized by a parameter q.

Purpose of the Study:

  • To investigate the free energy of the random energy model within the framework of nonextensive statistical mechanics.
  • To determine the influence of the nonextensivity parameter q on the system's phase behavior.

Main Methods:

  • Analytical derivation of the free energy for the random energy model.
  • Analysis of the obtained free energy expression for different values of the parameter q.

Main Results:

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  • The free energy of the random energy model was successfully derived for various values of the parameter q.
  • The study identified distinct phase transitions governed by the parameter q.

Conclusions:

  • The system exhibits either paramagnetic or spin-glass phases.
  • The specific phase is critically dependent on the value of the nonextensivity parameter q, highlighting the role of nonextensive statistical mechanics in understanding complex systems.